17 September 2021  11:53:57.511 PM
 
test_min_test
  FORTRAN90 version
  Test the TEST_MIN library.
 
p00_title_test
  For each problem, print the title.
 
   Problem Title
 
         1  Simple quadratic, (x-2)^2+1.
         2  Quadratic plus exponential, x^2 + e^(-x).
         3  Quartic, x^4 + 2x^2 + x + 3.
         4  Steep valley, e^x + 1/(100x).
         5  Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2)
         6  line, 2 - x.
         7  The dying snake, ( x + sin(x) ) * e^(-x^2).
         8  The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4
         9  The oscillatory parabola
        10  The cosine combo
        11  1 + |3x-1|
        12  The fuzzy parabola
        13  The lazy W
        14  Humps
 
TEST02
  For each problem, evaluate the function
  at the starting point and the solution.
 
  Problem        1
  Simple quadratic, (x-2)^2+1.
 
    F(X_START)=   2.3032338    
    F(X_SOL)=     1.0000000    
 
  Problem        2
  Quadratic plus exponential, x^2 + e^(-x).
 
    F(X_START)=   1.0893290    
    F(X_SOL)=    0.82718403    
 
  Problem        3
  Quartic, x^4 + 2x^2 + x + 3.
 
    F(X_START)=   14.062500    
    F(X_SOL)=     2.8784928    
 
  Problem        4
  Steep valley, e^x + 1/(100x).
 
    F(X_START)=   2.5962360    
    F(X_SOL)=     1.2049206    
 
  Problem        5
  Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2)
 
    F(X_START)=   1.4883553    
    F(X_SOL)=    0.62802572    
 
  Problem        6
  line, 2 - x.
 
    F(X_START)=  -5.2000000    
    F(X_SOL)=    -7.0000000    
 
  Problem        7
  The dying snake, ( x + sin(x) ) * e^(-x^2).
 
    F(X_START)= -0.56122233E-10
    F(X_SOL)=   -0.82423940    
 
  Problem        8
  The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4
 
    F(X_START)=   29.764712    
    F(X_SOL)=    -10000.000    
 
  Problem        9
  The oscillatory parabola
 
    F(X_START)=   9.3657292    
    F(X_SOL)=    -9.9779149    
 
  Problem       10
  The cosine combo
 
    F(X_START)=  -1.3359272    
    F(X_SOL)=    -13.079734    
 
  Problem       11
  1 + |3x-1|
 
    F(X_START)=   2.2500000    
    F(X_SOL)=     1.0000000    
 
  Problem       12
  The fuzzy parabola
 
    F(X_START)=   1.3959252    
    F(X_SOL)=   -0.99209999    
 
  Problem       13
  The lazy W
 
    F(X_START)=   4.6302000    
    F(X_SOL)=    -5.2430721    
 
  Problem       14
  Humps
 
    F(X_START)=   47.448276    
    F(X_SOL)=     11.252754    
 
TEST03
  For each problem, compare the exact and
  approximate gradients at the starting point.
 
  Problem        1
  Simple quadratic, (x-2)^2+1.
 
  X
       3.1415927    
  F'(X) (exact)
       2.2831853    
  F'(X) (difference)
       2.2831853    
 
  Problem        2
  Quadratic plus exponential, x^2 + e^(-x).
 
  X
      0.80000000    
  F'(X) (exact)
       1.1506710    
  F'(X) (difference)
       1.1506710    
 
  Problem        3
  Quartic, x^4 + 2x^2 + x + 3.
 
  X
       1.5000000    
  F'(X) (exact)
       20.500000    
  F'(X) (difference)
       20.500000    
 
  Problem        4
  Steep valley, e^x + 1/(100x).
 
  X
      0.95000000    
  F'(X) (exact)
       2.5746293    
  F'(X) (difference)
       2.5746293    
 
  Problem        5
  Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2)
 
  X
       1.5000000    
  F'(X) (exact)
       2.4772452    
  F'(X) (difference)
       2.4772452    
 
  Problem        6
  line, 2 - x.
 
  X
       7.2000000    
  F'(X) (exact)
      -1.0000000    
  F'(X) (difference)
      -1.0000000    
 
  Problem        7
  The dying snake, ( x + sin(x) ) * e^(-x^2).
 
  X
      -5.0000000    
  F'(X) (exact)
     -0.54339490E-09
  F'(X) (difference)
     -0.54339491E-09
 
  Problem        8
  The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4
 
  X
       3.1000000    
  F'(X) (exact)
       18.106356    
  F'(X) (difference)
       18.106356    
 
  Problem        9
  The oscillatory parabola
 
  X
      -2.0000000    
  F'(X) (exact)
       55.069777    
  F'(X) (difference)
       55.069777    
 
  Problem       10
  The cosine combo
 
  X
      0.50000000    
  F'(X) (exact)
       41.225360    
  F'(X) (difference)
       41.225360    
 
  Problem       11
  1 + |3x-1|
 
  X
      0.75000000    
  F'(X) (exact)
       3.0000000    
  F'(X) (difference)
       3.0000000    
 
  Problem       12
  The fuzzy parabola
 
  X
       1.0000000    
  F'(X) (exact)
      -50.668988    
  F'(X) (difference)
      -46.668983    
 
  Problem       13
  The lazy W
 
  X
     -0.10000000    
  F'(X) (exact)
       4.3920000    
  F'(X) (difference)
       4.3920000    
 
  Problem       14
  Humps
 
  X
      0.40000000    
  F'(X) (exact)
      -488.10939    
  F'(X) (difference)
      -488.10939    
 
TEST04
  For each problem, compare the exact and
  approximate second derivatives at the starting point.
 
  Problem        1
  Simple quadratic, (x-2)^2+1.
 
  X:
       3.1415927    
  F"(X) (exact):
       2.0000    
  F"(X) (difference):
       2.0000    
 
  Problem        2
  Quadratic plus exponential, x^2 + e^(-x).
 
  X:
      0.80000000    
  F"(X) (exact):
       2.4493    
  F"(X) (difference):
       2.4493    
 
  Problem        3
  Quartic, x^4 + 2x^2 + x + 3.
 
  X:
       1.5000000    
  F"(X) (exact):
       31.000    
  F"(X) (difference):
       31.000    
 
  Problem        4
  Steep valley, e^x + 1/(100x).
 
  X:
      0.95000000    
  F"(X) (exact):
       2.6090    
  F"(X) (difference):
       2.6090    
 
  Problem        5
  Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2)
 
  X:
       1.5000000    
  F"(X) (exact):
       4.4876    
  F"(X) (difference):
       4.4876    
 
  Problem        6
  line, 2 - x.
 
  X:
       7.2000000    
  F"(X) (exact):
       0.0000    
  F"(X) (difference):
       0.0000    
 
  Problem        7
  The dying snake, ( x + sin(x) ) * e^(-x^2).
 
  X:
      -5.0000000    
  F"(X) (exact):
      0.83979E-08
  F"(X) (difference):
     -0.51567E-08
 
  Problem        8
  The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4
 
  X:
       3.1000000    
  F"(X) (exact):
      -5.8685    
  F"(X) (difference):
      -5.8685    
 
  Problem        9
  The oscillatory parabola
 
  X:
      -2.0000000    
  F"(X) (exact):
      -277.80    
  F"(X) (difference):
      -277.80    
 
  Problem       10
  The cosine combo
 
  X:
      0.50000000    
  F"(X) (exact):
       177.65    
  F"(X) (difference):
       177.65    
 
  Problem       11
  1 + |3x-1|
 
  X:
      0.75000000    
  F"(X) (exact):
       0.0000    
  F"(X) (difference):
       0.0000    
 
  Problem       12
  The fuzzy parabola
 
  X:
       1.0000000    
  F"(X) (exact):
      -1110.2    
  F"(X) (difference):
      -1110.2    
 
  Problem       13
  The lazy W
 
  X:
     -0.10000000    
  F"(X) (exact):
      -13.760    
  F"(X) (difference):
      -13.760    
 
  Problem       14
  Humps
 
  X:
      0.40000000    
  F"(X) (exact):
       5058.2    
  F"(X) (difference):
       5058.2    
 
TEST05
  For each problem, take a few steps of 
  the bisection method.
 
  Problem        1
  Simple quadratic, (x-2)^2+1.
 
     0
  X: 0.000000000     1.570796327     3.141592654    
  F: 5.000000000     1.184215793     2.303233787    
     1
  X: 1.570796327     2.356194490     3.141592654    
  F: 1.184215793     1.126874515     2.303233787    
     2
  X: 1.570796327     1.963495408     2.356194490    
  F: 1.184215793     1.001332585     1.126874515    
     3
  X: 1.767145868     1.963495408     2.159844949    
  F: 1.054221047     1.001332585     1.025550408    
     4
  X: 1.865320638     1.963495408     2.061670179    
  F: 1.018138531     1.001332585     1.003803211    
     5
  X: 1.963495408     2.012582794     2.061670179    
  F: 1.001332585     1.000158327     1.003803211    
     6
  X: 1.963495408     1.988039101     2.012582794    
  F: 1.001332585     1.000143063     1.000158327    
     7
  X: 1.988039101     2.000310947     2.012582794    
  F: 1.000143063     1.000000097     1.000158327    
     8
  X: 1.994175024     2.000310947     2.006446871    
  F: 1.000033930     1.000000097     1.000041562    
     9
  X: 1.997242986     2.000310947     2.003378909    
  F: 1.000007601     1.000000097     1.000011417    
    10
  X: 1.998776967     2.000310947     2.001844928    
  F: 1.000001496     1.000000097     1.000003404    
 
  Problem        2
  Quadratic plus exponential, x^2 + e^(-x).
 
     0
  X: 0.000000000    0.5000000000     1.000000000    
  F: 1.000000000    0.8565306597     1.367879441    
     1
  X: 0.000000000    0.2500000000    0.5000000000    
  F: 1.000000000    0.8413007831    0.8565306597    
     2
  X:0.2500000000    0.3750000000    0.5000000000    
  F:0.8413007831    0.8279142788    0.8565306597    
     3
  X:0.3125000000    0.3750000000    0.4375000000    
  F:0.8292718789    0.8279142788    0.8370547764    
     4
  X:0.3125000000    0.3437500000    0.3750000000    
  F:0.8292718789    0.8272702449    0.8279142788    
     5
  X:0.3437500000    0.3593750000    0.3750000000    
  F:0.8272702449    0.8272629007    0.8279142788    
     6
  X:0.3437500000    0.3515625000    0.3593750000    
  F:0.8272702449    0.8271840658    0.8272629007    
     7
  X:0.3476562500    0.3515625000    0.3554687500    
  F:0.8272065076    0.8271840658    0.8272028774    
     8
  X:0.3496093750    0.3515625000    0.3535156250    
  F:0.8271901274    0.8271840658    0.8271883175    
     9
  X:0.3505859375    0.3515625000    0.3525390625    
  F:0.8271858071    0.8271840658    0.8271849028    
    10
  X:0.3510742188    0.3515625000    0.3520507812    
  F:0.8271846141    0.8271840658    0.8271841620    
 
  Problem        3
  Quartic, x^4 + 2x^2 + x + 3.
 
     0
  X:-2.000000000     0.000000000     2.000000000    
  F: 25.00000000     3.000000000     29.00000000    
     1
  X:-1.000000000     0.000000000     1.000000000    
  F: 5.000000000     3.000000000     7.000000000    
     2
  X:-.5000000000     0.000000000    0.5000000000    
  F: 3.062500000     3.000000000     4.062500000    
     3
  X:-.5000000000    -.2500000000     0.000000000    
  F: 3.062500000     2.878906250     3.000000000    
     4
  X:-.3750000000    -.2500000000    -.1250000000    
  F: 2.926025391     2.878906250     2.906494141    
     5
  X:-.3125000000    -.2500000000    -.1875000000    
  F: 2.892349243     2.878906250     2.884048462    
     6
  X:-.2812500000    -.2500000000    -.2187500000    
  F: 2.883210182     2.878906250     2.879242897    
     7
  X:-.2500000000    -.2343750000    -.2187500000    
  F: 2.878906250     2.878505766     2.879242897    
     8
  X:-.2421875000    -.2343750000    -.2265625000    
  F: 2.878562454     2.878505766     2.878733460    
     9
  X:-.2421875000    -.2382812500    -.2343750000    
  F: 2.878562454     2.878498394     2.878505766    
    10
  X:-.2382812500    -.2363281250    -.2343750000    
  F: 2.878498394     2.878493173     2.878505766    
 
  Problem        4
  Steep valley, e^x + 1/(100x).
 
     0
  X:0.1000000000E-030.5000500000     1.000000000    
  F: 101.0001000     1.668801709     2.728281828    
     1
  X:0.1000000000E-030.2500750000    0.5000500000    
  F: 101.0001000     1.324109726     1.668801709    
     2
  X:0.1000000000E-030.1250875000    0.2500750000    
  F: 101.0001000     1.213191647     1.324109726    
     3
  X:0.6259375000E-010.1250875000    0.1875812500    
  F: 1.224354619     1.213191647     1.259638492    
     4
  X:0.6259375000E-010.9384062500E-010.1250875000    
  F: 1.224354619     1.204948332     1.213191647    
     5
  X:0.7821718750E-010.9384062500E-010.1094640625    
  F: 1.209206629     1.204948332     1.207034158    
     6
  X:0.8602890625E-010.9384062500E-010.1016523437    
  F: 1.206077830     1.204948332     1.205373065    
     7
  X:0.8993476562E-010.9384062500E-010.9774648437E-01
  F: 1.205294614     1.204948332     1.204988672    
     8
  X:0.9384062500E-010.9579355469E-010.9774648437E-01
  F: 1.204948332     1.204922998     1.204988672    
     9
  X:0.9481708984E-010.9579355469E-010.9677001953E-01
  F: 1.204923954     1.204922998     1.204944787    
    10
  X:0.9481708984E-010.9530532227E-010.9579355469E-01
  F: 1.204923954     1.204920591     1.204922998    
 
  Problem        5
  Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2)
 
     0
  X:0.2000000000E-03 1.000100000     2.000000000    
  F: 25.99980002    0.7283516705     3.394055849    
     1
  X:0.2000000000E-030.5001500000     1.000100000    
  F: 25.99980002    0.6686586016    0.7283516705    
     2
  X:0.5001500000    0.7501250000     1.000100000    
  F:0.6686586016    0.6303439925    0.7283516705    
     3
  X:0.6251375000    0.7501250000    0.8751125000    
  F:0.6342217808    0.6303439925    0.6603459791    
     4
  X:0.6251375000    0.6876312500    0.7501250000    
  F:0.6342217808    0.6282765718    0.6303439925    
     5
  X:0.6563843750    0.6876312500    0.7188781250    
  F:0.6302733868    0.6282765718    0.6282820645    
     6
  X:0.6876312500    0.7032546875    0.7188781250    
  F:0.6282765718    0.6280257232    0.6282820645    
     7
  X:0.6954429687    0.7032546875    0.7110664062    
  F:0.6280881702    0.6280257232    0.6280900704    
     8
  X:0.6993488281    0.7032546875    0.7071605469    
  F:0.6280411502    0.6280257232    0.6280419945    
     9
  X:0.7013017578    0.7032546875    0.7052076172    
  F:0.6280294810    0.6280257232    0.6280298899    
    10
  X:0.7022782227    0.7032546875    0.7042311523    
  F:0.6280266123    0.6280257232    0.6280268152    
 
  Problem        6
  line, 2 - x.
 
     0
  X: 7.000000000     8.000000000     9.000000000    
  F:-5.000000000    -6.000000000    -7.000000000    
     1
  X: 8.000000000     8.500000000     9.000000000    
  F:-6.000000000    -6.500000000    -7.000000000    
     2
  X: 8.500000000     8.750000000     9.000000000    
  F:-6.500000000    -6.750000000    -7.000000000    
     3
  X: 8.750000000     8.875000000     9.000000000    
  F:-6.750000000    -6.875000000    -7.000000000    
     4
  X: 8.875000000     8.937500000     9.000000000    
  F:-6.875000000    -6.937500000    -7.000000000    
     5
  X: 8.937500000     8.968750000     9.000000000    
  F:-6.937500000    -6.968750000    -7.000000000    
     6
  X: 8.968750000     8.984375000     9.000000000    
  F:-6.968750000    -6.984375000    -7.000000000    
     7
  X: 8.984375000     8.992187500     9.000000000    
  F:-6.984375000    -6.992187500    -7.000000000    
     8
  X: 8.992187500     8.996093750     9.000000000    
  F:-6.992187500    -6.996093750    -7.000000000    
     9
  X: 8.996093750     8.998046875     9.000000000    
  F:-6.996093750    -6.998046875    -7.000000000    
    10
  X: 8.998046875     8.999023438     9.000000000    
  F:-6.998046875    -6.999023438    -7.000000000    
 
  Problem        7
  The dying snake, ( x + sin(x) ) * e^(-x^2).
 
     0
  X:-10.00000000     0.000000000     10.00000000    
  F:-.3517695990E-42 0.000000000    0.3517695990E-42
     1
  X:-10.00000000    -5.000000000     0.000000000    
  F:-.3517695990E-42-.5612223283E-10 0.000000000    
     2
  X:-5.000000000    -2.500000000     0.000000000    
  F:-.5612223283E-10-.5981458367E-02 0.000000000    
     3
  X:-2.500000000    -1.250000000     0.000000000    
  F:-.5981458367E-02-.4609322164     0.000000000    
     4
  X:-1.250000000    -.6250000000     0.000000000    
  F:-.4609322164    -.8187927720     0.000000000    
     5
  X:-.9375000000    -.6250000000    -.3125000000    
  F:-.7239990899    -.8187927720    -.5622598182    
     6
  X:-.7812500000    -.6250000000    -.4687500000    
  F:-.8068191985    -.8187927720    -.7389378105    
     7
  X:-.7812500000    -.7031250000    -.6250000000    
  F:-.8068191985    -.8232622828    -.8187927720    
     8
  X:-.7031250000    -.6640625000    -.6250000000    
  F:-.8232622828    -.8238067839    -.8187927720    
     9
  X:-.7031250000    -.6835937500    -.6640625000    
  F:-.8232622828    -.8242107028    -.8238067839    
    10
  X:-.6933593750    -.6835937500    -.6738281250    
  F:-.8239030163    -.8242107028    -.8241802528    
 
  Problem        8
  The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4
 
     0
  X: 2.000000000     3.000000000     4.000000000    
  F: 13.00271893     27.95986410     48.99686525    
     1
  X: 2.000000000     2.500000000     3.000000000    
  F: 13.00271893     19.74088788     27.95986410    
     2
  X: 2.000000000     2.250000000     2.500000000    
  F: 13.00271893     16.18514404     19.74088788    
     3
  X: 2.000000000     2.125000000     2.250000000    
  F: 13.00271893     14.54721288     16.18514404    
     4
  X: 2.000000000     2.062500000     2.125000000    
  F: 13.00271893     13.76328165     14.54721288    
     5
  X: 2.000000000     2.031250000     2.062500000    
  F: 13.00271893     13.38007874     13.76328165    
     6
  X: 2.000000000     2.015625000     2.031250000    
  F: 13.00271893     13.19066839     13.38007874    
     7
  X: 2.000000000     2.007812500     2.015625000    
  F: 13.00271893     13.09651104     13.19066839    
     8
  X: 2.000000000     2.003906250     2.007812500    
  F: 13.00271893     13.04956933     13.09651104    
     9
  X: 2.000000000     2.001953125     2.003906250    
  F: 13.00271893     13.02613272     13.04956933    
    10
  X: 2.000000000     2.000976562     2.001953125    
  F: 13.00271893     13.01442297     13.02613272    
 
  Problem        9
  The oscillatory parabola
 
     0
  X:-5.000000000     0.000000000     5.000000000    
  F: 34.16521548    -9.092974268     30.36572918    
     1
  X:-2.500000000     0.000000000     2.500000000    
  F: 6.670243527    -9.092974268    -.5663876002    
     2
  X:-1.250000000     0.000000000     1.250000000    
  F:-7.006959789    -9.092974268     3.426532968    
     3
  X:-.6250000000     0.000000000    0.6250000000    
  F: 9.409124422    -9.092974268    -4.540161858    
     4
  X:-.3125000000     0.000000000    0.3125000000    
  F:-.9646992790    -9.092974268    -9.070998694    
     5
  X: 0.000000000    0.1562500000    0.3125000000    
  F:-9.092974268    -9.974441032    -9.070998694    
     6
  X:0.7812500000E-010.1562500000    0.2343750000    
  F:-9.792706031    -9.974441032    -9.706242676    
     7
  X:0.1171875000    0.1562500000    0.1953125000    
  F:-9.944550012    -9.974441032    -9.891621180    
     8
  X:0.1367187500    0.1562500000    0.1757812500    
  F:-9.974187502    -9.974441032    -9.946502689    
     9
  X:0.1367187500    0.1464843750    0.1562500000    
  F:-9.974187502    -9.977914213    -9.974441032    
    10
  X:0.1416015625    0.1464843750    0.1513671875    
  F:-9.976960137    -9.977914213    -9.977068256    
 
  Problem       10
  The cosine combo
 
     0
  X: 0.000000000     3.500000000     7.000000000    
  F: 16.00000000     3.413260616     13.37906775    
     1
  X: 0.000000000     1.750000000     3.500000000    
  F: 16.00000000    -10.11534458     3.413260616    
     2
  X:0.8750000000     1.750000000     2.625000000    
  F:-1.797976827    -10.11534458    -.2586638168    
     3
  X: 1.312500000     1.750000000     2.187500000    
  F: 9.222517993    -10.11534458    -4.483175525    
     4
  X: 1.531250000     1.750000000     1.968750000    
  F: 4.726837494    -10.11534458    -5.228430928    
     5
  X: 1.640625000     1.750000000     1.859375000    
  F:-4.282425539    -10.11534458    -9.619438650    
     6
  X: 1.750000000     1.804687500     1.859375000    
  F:-10.11534458    -10.63046504    -9.619438650    
     7
  X: 1.777343750     1.804687500     1.832031250    
  F:-10.58245001    -10.63046504    -10.29139869    
     8
  X: 1.777343750     1.791015625     1.804687500    
  F:-10.58245001    -10.65739758    -10.63046504    
     9
  X: 1.784179688     1.791015625     1.797851562    
  F:-10.63289931    -10.65739758    -10.65640263    
    10
  X: 1.791015625     1.794433594     1.797851562    
  F:-10.65739758    -10.66005449    -10.65640263    
 
  Problem       11
  1 + |3x-1|
 
     0
  X: 0.000000000    0.5000000000     1.000000000    
  F: 2.000000000     1.500000000     3.000000000    
     1
  X: 0.000000000    0.2500000000    0.5000000000    
  F: 2.000000000     1.250000000     1.500000000    
     2
  X:0.2500000000    0.3750000000    0.5000000000    
  F: 1.250000000     1.125000000     1.500000000    
     3
  X:0.2500000000    0.3125000000    0.3750000000    
  F: 1.250000000     1.062500000     1.125000000    
     4
  X:0.3125000000    0.3437500000    0.3750000000    
  F: 1.062500000     1.031250000     1.125000000    
     5
  X:0.3125000000    0.3281250000    0.3437500000    
  F: 1.062500000     1.015625000     1.031250000    
     6
  X:0.3281250000    0.3359375000    0.3437500000    
  F: 1.015625000     1.007812500     1.031250000    
     7
  X:0.3281250000    0.3320312500    0.3359375000    
  F: 1.015625000     1.003906250     1.007812500    
     8
  X:0.3320312500    0.3339843750    0.3359375000    
  F: 1.003906250     1.001953125     1.007812500    
     9
  X:0.3320312500    0.3330078125    0.3339843750    
  F: 1.003906250     1.000976562     1.001953125    
    10
  X:0.3330078125    0.3334960938    0.3339843750    
  F: 1.000976562     1.000488281     1.001953125    
 
  Problem       12
  The fuzzy parabola
 
     0
  X:-2.000000000     0.000000000     2.000000000    
  F: 4.727142500     0.000000000     3.272857500    
     1
  X:-1.000000000     0.000000000     1.000000000    
  F:0.6040748498     0.000000000     1.395925150    
     2
  X:-1.000000000    -.5000000000     0.000000000    
  F:0.6040748498    -.7293576431     0.000000000    
     3
  X:-.7500000000    -.5000000000    -.2500000000    
  F:-.3244525138    -.7293576431    -.5691109877    
     4
  X:-.6250000000    -.5000000000    -.3750000000    
  F:-.5998299401    -.7293576431    -.7143196258    
     5
  X:-.5625000000    -.5000000000    -.4375000000    
  F: 1.315873932    -.7293576431     1.122117046    
     6
  X:-.5312500000    -.5000000000    -.4687500000    
  F:0.1644169120    -.7293576431    0.5047119934    
     7
  X:-.5156250000    -.5000000000    -.4843750000    
  F:-.5453352950    -.7293576431    -.2787736863    
     8
  X:-.5078125000    -.5000000000    -.4921875000    
  F:-.7200478149    -.7293576431    -.5730220284    
     9
  X:-.5078125000    -.5039062500    -.5000000000    
  F:-.7200478149    -.7460723883    -.7293576431    
    10
  X:-.5058593750    -.5039062500    -.5019531250    
  F:-.7383862570    -.7460723883    -.7430450359    
 
  Problem       13
  The lazy W
 
     0
  X:-2.000000000     0.000000000     2.000000000    
  F: 3.000000000     5.000000000     15.00000000    
     1
  X:-2.000000000    -1.000000000     0.000000000    
  F: 3.000000000    -3.000000000     5.000000000    
     2
  X:-2.000000000    -1.500000000    -1.000000000    
  F: 3.000000000    -5.125000000    -3.000000000    
     3
  X:-1.750000000    -1.500000000    -1.250000000    
  F:-2.929687500    -5.125000000    -4.804687500    
     4
  X:-1.500000000    -1.375000000    -1.250000000    
  F:-5.125000000    -5.210449219    -4.804687500    
     5
  X:-1.500000000    -1.437500000    -1.375000000    
  F:-5.125000000    -5.237274170    -5.210449219    
     6
  X:-1.437500000    -1.406250000    -1.375000000    
  F:-5.237274170    -5.240201950    -5.210449219    
     7
  X:-1.437500000    -1.421875000    -1.406250000    
  F:-5.237274170    -5.242952228    -5.240201950    
     8
  X:-1.429687500    -1.421875000    -1.414062500    
  F:-5.241183035    -5.242952228    -5.242614381    
     9
  X:-1.421875000    -1.417968750    -1.414062500    
  F:-5.242952228    -5.243044652    -5.242614381    
    10
  X:-1.421875000    -1.419921875    -1.417968750    
  F:-5.242952228    -5.243064030    -5.243044652    
 
  Problem       14
  Humps
 
     0
  X:0.3000000000    0.5500000000    0.8000000000    
  F: 96.50000000     13.94694960     17.84615385    
     1
  X:0.5500000000    0.6750000000    0.8000000000    
  F: 13.94694960     11.67348691     17.84615385    
     2
  X:0.5500000000    0.6125000000    0.6750000000    
  F: 13.94694960     11.44169063     11.67348691    
     3
  X:0.6125000000    0.6437500000    0.6750000000    
  F: 11.44169063     11.26645488     11.67348691    
     4
  X:0.6281250000    0.6437500000    0.6593750000    
  F: 11.27702751     11.26645488     11.40093307    
     5
  X:0.6281250000    0.6359375000    0.6437500000    
  F: 11.27702751     11.25310363     11.26645488    
     6
  X:0.6320312500    0.6359375000    0.6398437500    
  F: 11.26033509     11.25310363     11.25518850    
     7
  X:0.6359375000    0.6378906250    0.6398437500    
  F: 11.25310363     11.25299017     11.25518850    
     8
  X:0.6359375000    0.6369140625    0.6378906250    
  F: 11.25310363     11.25275687     11.25299017    
     9
  X:0.6364257813    0.6369140625    0.6374023438    
  F: 11.25285760     11.25275687     11.25280114    
    10
  X:0.6366699219    0.6369140625    0.6371582031    
  F: 11.25278909     11.25275687     11.25276089    
 
p00_fmin_test
  For each problem, use Brent's method.
 
  Problem        1
  Simple quadratic, (x-2)^2+1.
 
  Initial interval [A,B]:
 
   A,       B: 0.000000000                   3.141592654    
  FA,      FB: 5.000000000                   2.303233787    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B: 1.999999967     2.000000000     2.000000033    
  FA, FX*, FB: 1.000000000     1.000000000     1.000000000    
 
  Problem        2
  Quadratic plus exponential, x^2 + e^(-x).
 
  Initial interval [A,B]:
 
   A,       B: 0.000000000                   1.000000000    
  FA,      FB: 1.000000000                   1.367879441    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:0.3517337037    0.3517337123    0.3517337208    
  FA, FX*, FB:0.8271840261    0.8271840261    0.8271840261    
 
  Problem        3
  Quartic, x^4 + 2x^2 + x + 3.
 
  Initial interval [A,B]:
 
   A,       B:-2.000000000                   2.000000000    
  FA,      FB: 25.00000000                   29.00000000    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:-.2367329047    -.2367328978    -.2367328909    
  FA, FX*, FB: 2.878492790     2.878492790     2.878492790    
 
  Problem        4
  Steep valley, e^x + 1/(100x).
 
  Initial interval [A,B]:
 
   A,       B:0.1000000000E-03               1.000000000    
  FA,      FB: 101.0001000                   2.728281828    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:0.9534461248E-010.9534461724E-010.9534462199E-01
  FA, FX*, FB: 1.204920573     1.204920573     1.204920573    
 
  Problem        5
  Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2)
 
  Initial interval [A,B]:
 
   A,       B:0.2000000000E-03               2.000000000    
  FA,      FB: 25.99980002                   3.394055849    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:0.7032048265    0.7032048403    0.7032048542    
  FA, FX*, FB:0.6280257206    0.6280257206    0.6280257206    
 
  Problem        6
  line, 2 - x.
 
  Initial interval [A,B]:
 
   A,       B: 7.000000000                   9.000000000    
  FA,      FB:-5.000000000                  -7.000000000    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B: 8.999999589     8.999999746     9.000000000    
  FA, FX*, FB:-6.999999589    -6.999999746    -7.000000000    
 
  Problem        7
  The dying snake, ( x + sin(x) ) * e^(-x^2).
 
  Initial interval [A,B]:
 
   A,       B:-10.00000000                   10.00000000    
  FA,      FB:-.3517695990E-42              0.3517695990E-42
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:-.6795786730    -.6795786596    -.6795786461    
  FA, FX*, FB:-.8242393985    -.8242393985    -.8242393985    
 
  Problem        8
  The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4
 
  Initial interval [A,B]:
 
   A,       B: 2.000000000                   4.000000000    
  FA,      FB: 13.00271893                   48.99686525    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B: 2.000000000     2.000000060     2.000000097    
  FA, FX*, FB: 13.00271893     13.00271965     13.00272009    
 
  Problem        9
  The oscillatory parabola
 
  Initial interval [A,B]:
 
   A,       B:-5.000000000                   5.000000000    
  FA,      FB: 34.16521548                   30.36572918    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:-1.338452055    -1.338452016    -1.338451993    
  FA, FX*, FB:-8.197422376    -8.197422376    -8.197422376    
 
  Problem       10
  The cosine combo
 
  Initial interval [A,B]:
 
   A,       B: 0.000000000                   7.000000000    
  FA,      FB: 16.00000000                   13.37906775    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B: 1.016782047     1.016782065     1.016782084    
  FA, FX*, FB:-6.282750880    -6.282750880    -6.282750880    
 
  Problem       11
  1 + |3x-1|
 
  Initial interval [A,B]:
 
   A,       B: 0.000000000                   1.000000000    
  FA,      FB: 2.000000000                   3.000000000    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:0.3333333253    0.3333333378    0.3333333461    
  FA, FX*, FB: 1.000000024     1.000000014     1.000000038    
 
  Problem       12
  The fuzzy parabola
 
  Initial interval [A,B]:
 
   A,       B:-2.000000000                   2.000000000    
  FA,      FB: 4.727142500                   3.272857500    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:0.8884973490E-010.8884973956E-010.8884974421E-01
  FA, FX*, FB:-.9921001032    -.9921001032    -.9921001032    
 
  Problem       13
  The lazy W
 
  Initial interval [A,B]:
 
   A,       B:-2.000000000                   2.000000000    
  FA,      FB: 3.000000000                   15.00000000    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:-1.419234674    -1.419234626    -1.419234602    
  FA, FX*, FB:-5.243072144    -5.243072144    -5.243072144    
 
  Problem       14
  Humps
 
  Initial interval [A,B]:
 
   A,       B:0.3000000000                  0.8000000000    
  FA,      FB: 96.50000000                   17.84615385    
 
  Final interval [A,X*,B]:
 
   A,  X*,  B:0.6370089720    0.6370089848    0.6370089976    
  FA, FX*, FB: 11.25275413     11.25275413     11.25275413    
 
test_min_test
  Normal end of execution.
 
17 September 2021  11:53:57.512 PM