Average Error: 58.3 → 0.0
Time: 23.2s
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 r36495 = x;
        double r36496 = exp(r36495);
        double r36497 = -r36495;
        double r36498 = exp(r36497);
        double r36499 = r36496 - r36498;
        double r36500 = r36496 + r36498;
        double r36501 = r36499 / r36500;
        return r36501;
}
↓
double f(double x) {
        double r36502 = x;
        double r36503 = tanh(r36502);
        return r36503;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.3

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019208 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))