Skip to main content- abs
- Absolute value.
f' = sign(x), f'' = 0 (away from 0). At x = 0 the derivative is not defined; every surface takes the sub-gradient f'(0) = +1 (the x >= 0 branch), matching the winning-branch convention max/min use for payoffs. - acos
- Inverse cosine.
f' = -1/√(1-x²), f'' = x·f'³. - acosh
- Inverse hyperbolic cosine.
f' = 1/√(x²-1), f'' = -x·f'³. - asin
- Inverse sine.
f' = 1/√(1-x²), f'' = x·f'³. - asinh
- Inverse hyperbolic sine.
f' = 1/√(x²+1), f'' = -x·f'³. - atan
- Inverse tangent.
f' = 1/(1+x²), f'' = -2x·f'². - atan2
- atanh
- Inverse hyperbolic tangent.
f' = 1/(1-x²), f'' = 2x·f'². - cbrt
- Cube root.
f' = 1/(3·f²), f'' = -2/(9·x·f²). - cos
- Cosine.
- cosh
- Hyperbolic cosine.
- dot
- erf
- Gaussian error function.
f' = (2/√π)·e^{-x²}, f'' = -2x·f'. - erfc
- Complementary error function
1 - erf(x). f' = -(2/√π)·e^{-x²}. - exp
- Exponential.
f = f' = f''. - exp2
- Base-2 exponential.
f' = f·ln 2, f'' = f·(ln 2)². - exp_m1
exp(x) - 1. f' = f'' = exp(x) = f + 1.- hypot
- inv_norm_cdf
- Inverse standard normal CDF
Φ⁻¹(p). f' = 1/φ(f), f'' = f·f'². - ln
- Natural logarithm.
f' = 1/x, f'' = -1/x². - ln_1p
ln(1 + x). f' = 1/(1+x), f'' = -f'².- log2
- Base-2 logarithm.
f' = 1/(x·ln 2), f'' = -f'/x. - log10
- Base-10 logarithm.
f' = 1/(x·ln 10), f'' = -f'/x. - max
- min
- norm_cdf
- Standard normal CDF
Φ(x). f' = φ(x), f'' = -x·φ(x). - norm_pdf
- Standard normal density
φ(x). f' = -x·φ(x), f'' = (x² − 1)·φ(x). - pow
- powf
- powi
- sin
- Sine.
- sinh
- Hyperbolic sine.
- sqrt
- Square root.
f' = 1/(2√x), f'' = -1/(4·x·√x). - sum
- tan
- Tangent.
f' = 1 + tan², f'' = 2·tan·f'. - tanh
- Hyperbolic tangent.
f' = 1 - tanh², f'' = -2·tanh·f'. - weighted_dot
- weighted_sum