Average Error: 0.0 → 0.2
Time: 2.3s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\log \left(e^{\frac{2}{e^{x} + e^{-x}}}\right)\]
\frac{2}{e^{x} + e^{-x}}
↓
\log \left(e^{\frac{2}{e^{x} + e^{-x}}}\right)
double code(double x) {
	return ((double) (2.0 / ((double) (((double) exp(x)) + ((double) exp(((double) -(x))))))));
}
↓
double code(double x) {
	return ((double) log(((double) exp(((double) (2.0 / ((double) (((double) exp(x)) + ((double) exp(((double) -(x))))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied add-log-exp0.2

    \[\leadsto \color{blue}{\log \left(e^{\frac{2}{e^{x} + e^{-x}}}\right)}\]

  4. Final simplification0.2

    \[\leadsto \log \left(e^{\frac{2}{e^{x} + e^{-x}}}\right)\]

Reproduce

herbie shell --seed 2020120 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))