Average Error: 58.2 → 0.0
Time: 19.3s
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 r2637241 = x;
        double r2637242 = exp(r2637241);
        double r2637243 = -r2637241;
        double r2637244 = exp(r2637243);
        double r2637245 = r2637242 - r2637244;
        double r2637246 = r2637242 + r2637244;
        double r2637247 = r2637245 / r2637246;
        return r2637247;
}
↓
double f(double x) {
        double r2637248 = x;
        double r2637249 = tanh(r2637248);
        return r2637249;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019172 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))