Member Avatar for Hawkeye Python

When realising the following operation:

do = 1.0 - 2.718281828**(-(23**2)/730)
print do

Python returns 0.632120558766

When you do it on the calculator or when google it, it returns 0.515509538

:-O

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  • Latest Post Latest Post by vegaseat

Dani AI

Generated

Short answer: this is not a math bug but integer (classic) division in Python 2. The sub-expression is evaluated with integer operands, so the sequence is: 23**2 -> 529, apply unary minus -> -529, then integer division -529/730 floors to -1 — which makes the exponent be -1 and yields the ~0.632 value you saw. (peps.python.org)

What to do:

  • Make the division a floating-point division (ensure one operand is a float or use float()), or enable true division with from __future__ import division in Python 2, or run the code under Python 3 (where / already means true division). , and pointed this out earlier. (peps.python.org)

For clearer, safer math use the math module instead of typing an approximate e and raising it manually. Also prefer expm1 when you compute 1 - exp(-y) for small y to avoid loss of precision (it computes exp(x)-1 more accurately). Example (avoids repeating the forum snippets):

import math

y = float(23 * 23) / 730.0
# numerically stable and explicit:
result = -math.expm1(-y)   # equal to 1 - math.exp(-y), but more accurate for small y
print(result)

See the Python math docs for exp, expm1 and the e constant for details. (docs.python.org)

Quick checklist when results look wrong:

  • Print intermediate values and types to see where integer division happens.
  • Make at least one operand float (or use float()).
  • Prefer math.exp/math.expm1 and math.e for readability and numerical stability.
  • In legacy code, consider from __future__ import division or migrating to Python 3. (peps.python.org)

Recommended Answers

All 5 Replies

Member Avatar for snippsat 
>>> 1.0 - 2.718281828**(-(23.0**2)/730)
0.5155095380022271
>>> #Or import division from future
>>> from __future__ import division
>>> 1.0 - 2.718281828**(-(23**2)/730)
0.5155095380022271
>>>

Edited by snippsat because: n/a
Member Avatar for woooee

"/ 730" has to be a float (or you have to convert somehow).

##1.0 - 2.718281828**(-(23**2)/730)
a = 23**2
print a
a *= -1
print a
print "---------------"
print a/730
a /= 730.0
print a
print "---------------"
b =  2.718281828**a
print b
print 1.0 - b
Edited by woooee because: n/a
Member Avatar for vegaseat

Something like
q = 3/5
would signify a division of integers and would give you
q = 0
in most computer languages and Python2

Python3 has changed this '/' is now a floating point division and '//' is an integer division.

If you want q to be a floating point in Python2, then you simply use
q = 3/5.0

print (23**2)/730     # 0
print (23**2)/730.0   # 0.724657534247
Edited by vegaseat because: n/a
Member Avatar for Hawkeye Python

Oh... I though that using

.0

in only one element was enough. Tks

Member Avatar for vegaseat

The compiler will take your math expression and turn it into a series of smaller stepwise expressions. That one time .0 can easily get lost. Anyway, Python3 takes care of that ambiguity.

Edited by vegaseat because: n/a
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