Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
Cost: 6592
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{1}{\cosh x}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{1}{\cosh x}
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x) :precision binary64 (/ 1.0 (cosh x)))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return 1.0 / cosh(x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.4
Cost1090
\[\begin{array}{l} \mathbf{if}\;x \leq -1.4015561200794018:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 1.4186901835741934:\\ \;\;\;\;1 - 0.5 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 2
Error0.5
Cost706
\[\begin{array}{l} \mathbf{if}\;x \leq -359.26091895379255:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 357.8019380154624:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 3
Error30.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied clear-num_binary64_14410.0

    \[\leadsto \color{blue}{\frac{1}{\frac{e^{x} + e^{-x}}{2}}}\]

  4. Simplified0.0

    \[\leadsto \frac{1}{\color{blue}{\cosh x}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{\frac{1}{\cosh x}}\]

  6. Final simplification0.0

    \[\leadsto \frac{1}{\cosh x}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))