Average Error: 58.1 → 0.0
Time: 19.6s
Precision: 64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[\tanh x\]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
\tanh x
double f(double x) {
        double r1592945 = x;
        double r1592946 = exp(r1592945);
        double r1592947 = -r1592945;
        double r1592948 = exp(r1592947);
        double r1592949 = r1592946 - r1592948;
        double r1592950 = r1592946 + r1592948;
        double r1592951 = r1592949 / r1592950;
        return r1592951;
}
↓
double f(double x) {
        double r1592952 = x;
        double r1592953 = tanh(r1592952);
        return r1592953;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

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

  3. Applied tanh-undef0.0

    \[\leadsto \color{blue}{\tanh x}\]

  4. Final simplification0.0

    \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2019139 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))