Reference · Math

math.expm1

math.expm1(num) -> float

What it does

e to the power of the number, minus one, as a float, as Python's math.expm1. For a number close to zero the answer is accurate where math.exp(x) - 1 is not, since the subtraction there throws away most of the digits. Its inverse is math.log1p.

Examples

print(math.expm1(0), math.expm1(1), math.expm1(-1))print(math.expm1(1e-10), math.exp(1e-10) - 1)

0.0 1.718281828459045 -0.63212055882855770.000000000100000000005 0.0000000001000000082740371

Edge cases

• math.exp(1e-16) - 1 is 0.0; math.expm1(1e-16) keeps the value.
• A large negative number gives -1.0, and so does -inf: underflow is not an error.
• 709 is about the largest input that fits a float; 710 is a range error.
• math.log1p undoes it: math.log1p(math.expm1(x)) is x.

print(math.exp(1e-16) - 1, math.expm1(1e-16))print(math.expm1(-1000), math.expm1(-math.inf), math.isfinite(math.expm1(709)))print(math.log1p(math.expm1(0.3)), math.expm1(math.nan))

0.0 0.0000000000000001-1.0 -1.0 true0.3 NaN

Errors

A result past the largest float is a runtime error (a range error), not an error value: it stops the request. A value that is not a number is a runtime error too.

print(math.expm1(710))

line 1: `math.expm1`: math range error (710)

Chaining

Continuous growth at a rate over a time is math.expm1(rate * t), which for a small rate keeps the growth exact:

let rate = 0.0001print(rate * 2 | math.expm1)print([0, 0.5, 1] | map(math.expm1))

0.00020002000133340002[0.0, 0.6487212707001282, 1.718281828459045]

See also

math.exp, math.log1p, math.log

Edit this page on GitHub · every example's output was made by running it (tools/refcheck.mjs) · questions on Discord or r/quillo