Average Error: 58.1 → 0.0
Time: 23.1s
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 r36247 = x;
        double r36248 = exp(r36247);
        double r36249 = -r36247;
        double r36250 = exp(r36249);
        double r36251 = r36248 - r36250;
        double r36252 = r36248 + r36250;
        double r36253 = r36251 / r36252;
        return r36253;
}
↓
double f(double x) {
        double r36254 = x;
        double r36255 = tanh(r36254);
        return r36255;
}

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 2019209 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))