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Python preflop error overflow error

StackOverflow has quite a few topics for floating point representations, exceptions, truncations, and precision issues. I tried to explain this, but still do not understand.

from operator import add, sub, mul, div

fun = 'add(add(sub(sub(safeDiv(xL1, add(D, mul(sub(add(sub(A, 0), mul(D, rv)), mul(xL1, add(D, 3))), xL1))), add(0, rv)), safeDiv(mul(sub(D, sigma2), safeDiv(sub(safeDiv(xL1, A), 1), add(safeDiv(safeDiv(B1, xL1), sub(4, xL2)), add(sigma1, xL1)))), sigma1)), add(4, B1)), add(add(A, A), sub(add(xL1, xL1), mul(xL2, safeDiv(xL1, add(sub(add(mul(D, -4), add(add(safeDiv(mul(sigma2, sigma2), safeDiv(B1, sigma1)), sub(add(D, safeDiv(xL2, B1)), D)), sub(4, B1))), A), add(mul(sigma2, xL1), mul(xL1, mul(rv, xL2)))))))))'

d = [(
51.696521954140991,
31.156112806482234,
54.629863633907163,
27.491618858013698,
26.223584534107289,
77.10005191617563,
2708.4145268939428,
0.20952943771134946,
15.558278150405643,
102.0,
225.0)]

arglabels = ['xL1', 'sigma1', 'xL2', 'sigma2', 'A', 'B1', 'D', 'rv']
other = {'add': add, 'sub':sub, 'mul':mul,'safeDiv':div}
inputs = dict(zip(arglabels, d[0][: -4] + (d[0][-3]*d[0][-4],)))
inputs.update(other)
print eval(fun, inputs)

This code should give a result somewhere between 225 and 240, but instead returns a negative number. And that this, no exception, no warning, nothing. So it should be the accuracy of the error somewhere that completely disables the result.

When rounding the maximum that I can use to get a reasonable result, this is 1 decimal place (and this brings me closer to 207 ...), in some cases doubles the amount of help, but this is not enough. I did it manually (so a significant loss of accuracy and got 240).

, script :

locals , , . - , , .

, ? - ? , ?

: , . , (). , MathOverflow...

+4
2

225...240, :

  • fun
  • d
  • add, sub, mul safeDiv - , , , .

, , , -2786.17215265, . . script , . , . :

add: -10626.8589858 + 10627.794501 = 0.935515251547

, .

C (MATLAB/Octave).

, . Out[108] Out[110], , ds data[17]. Out[109] Out[110], rv, In[110]. , , Out[109] (230.62977145178198) , rv : 4.075164147, 4.485709922, 51.72476610, ​​ script .

, fun rv, ( 3.3 51.7). , .

from operator import add, sub, mul, div

fun = 'add(add(sub(sub(safeDiv(xL1, add(D, mul(sub(add(sub(A, 0), mul(D, rv)), mul(xL1, add(D, 3))), xL1))), add(0, rv)), safeDiv(mul(sub(D, sigma2), safeDiv(sub(safeDiv(xL1, A), 1), add(safeDiv(safeDiv(B1, xL1), sub(4, xL2)), add(sigma1, xL1)))), sigma1)), add(4, B1)), add(add(A, A), sub(add(xL1, xL1), mul(xL2, safeDiv(xL1, add(sub(add(mul(D, -4), add(add(safeDiv(mul(sigma2, sigma2), safeDiv(B1, sigma1)), sub(add(D, safeDiv(xL2, B1)), D)), sub(4, B1))), A), add(mul(sigma2, xL1), mul(xL1, mul(rv, xL2)))))))))'

d = [(
51.696521954140991,
31.156112806482234,
54.629863633907163,
27.491618858013698,
26.223584534107289,
77.10005191617563,
2708.4145268939428,
0.20952943771134946,
15.558278150405643,
102.0,
225.0)]

def add_verbose(a,b):
    res = a + b;
    print "add: {0} + {1} = {2}".format(a,b,res);
    return res;

def sub_verbose(a,b):
    res = a - b;
    print "sub: {0} - {1} = {2}".format(a,b,res);
    return res;

def div_verbose(a,b):
    res = a / b;
    print "div: {0} / {1} = {2}".format(a,b,res);
    return res;

def mul_verbose(a,b):
    res = a * b;
    print "mul: {0} * {1} = {2}".format(a,b,res);
    return res;

arglabels = ['xL1', 'sigma1', 'xL2', 'sigma2', 'A', 'B1', 'D', 'rv']
other = {'add': add_verbose, 'sub':sub_verbose, 'mul':mul_verbose,'safeDiv':div_verbose}
inputs = dict(zip(arglabels, d[0][: -4] + (d[0][-3]*d[0][-4],)))
inputs.update(other)

# out 108
print eval(fun, inputs)

# set locals that can give out 109
safeDiv = div;
rv = 4.0751641470166795256;
inputs.update(locals());

# out 109
print eval(fun, inputs)


sub: 26.2235845341 - 0 = 26.2235845341
mul: 2708.41452689 * 3.25991727261 = 8829.20729761
add: 26.2235845341 + 8829.20729761 = 8855.43088215
add: 2708.41452689 + 3 = 2711.41452689
mul: 51.6965219541 * 2711.41452689 = 140170.700616
sub: 8855.43088215 - 140170.700616 = -131315.269734
mul: -131315.269734 * 51.6965219541 = -6788542.72473
add: 2708.41452689 + -6788542.72473 = -6785834.3102
div: 51.6965219541 / -6785834.3102 = -7.61830006318e-06
add: 0 + 3.25991727261 = 3.25991727261
sub: -7.61830006318e-06 - 3.25991727261 = -3.25992489091
sub: 2708.41452689 - 27.491618858 = 2680.92290804
div: 51.6965219541 / 26.2235845341 = 1.97137511414
sub: 1.97137511414 - 1 = 0.971375114142
div: 77.1000519162 / 51.6965219541 = 1.49139727397
sub: 4 - 54.6298636339 = -50.6298636339
div: 1.49139727397 / -50.6298636339 = -0.029456869265
add: 31.1561128065 + 51.6965219541 = 82.8526347606
add: -0.029456869265 + 82.8526347606 = 82.8231778914
div: 0.971375114142 / 82.8231778914 = 0.0117283004453
mul: 2680.92290804 * 0.0117283004453 = 31.4426693361
div: 31.4426693361 / 31.1561128065 = 1.00919744165
sub: -3.25992489091 - 1.00919744165 = -4.26912233256
add: 4 + 77.1000519162 = 81.1000519162
add: -4.26912233256 + 81.1000519162 = 76.8309295836
add: 26.2235845341 + 26.2235845341 = 52.4471690682
add: 51.6965219541 + 51.6965219541 = 103.393043908
mul: 2708.41452689 * -4 = -10833.6581076
mul: 27.491618858 * 27.491618858 = 755.789107434
div: 77.1000519162 / 31.1561128065 = 2.47463643475
div: 755.789107434 / 2.47463643475 = 305.414200171
div: 54.6298636339 / 77.1000519162 = 0.708558065477
add: 2708.41452689 + 0.708558065477 = 2709.12308496
sub: 2709.12308496 - 2708.41452689 = 0.708558065477
add: 305.414200171 + 0.708558065477 = 306.122758237
sub: 4 - 77.1000519162 = -73.1000519162
add: 306.122758237 + -73.1000519162 = 233.02270632
add: -10833.6581076 + 233.02270632 = -10600.6354013
sub: -10600.6354013 - 26.2235845341 = -10626.8589858
mul: 27.491618858 * 51.6965219541 = 1421.22107785
mul: 3.25991727261 * 54.6298636339 = 178.088836061
mul: 51.6965219541 * 178.088836061 = 9206.57342319
add: 1421.22107785 + 9206.57342319 = 10627.794501
add: -10626.8589858 + 10627.794501 = 0.935515251547
div: 51.6965219541 / 0.935515251547 = 55.2599456488
mul: 54.6298636339 * 55.2599456488 = 3018.84329521
sub: 103.393043908 - 3018.84329521 = -2915.4502513
add: 52.4471690682 + -2915.4502513 = -2863.00308224
add: 76.8309295836 + -2863.00308224 = -2786.17215265
-2786.17215265
230.629771452
+3

, :

>>> print eval(fun, inputs)
-2786.17215265

gmpy2 200 , - ~ 1E9, :

>>> print eval(fun,inputs)
-2786.1721526580839894614784542009831125135156833413835128962432

, . , , - .

@Prune .

+1

Source: https://habr.com/ru/post/1613418/

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