Average Error: 58.1 → 0.0
Time: 23.4s
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 r49458 = x;
        double r49459 = exp(r49458);
        double r49460 = -r49458;
        double r49461 = exp(r49460);
        double r49462 = r49459 - r49461;
        double r49463 = r49459 + r49461;
        double r49464 = r49462 / r49463;
        return r49464;
}
↓
double f(double x) {
        double r49465 = x;
        double r49466 = tanh(r49465);
        return r49466;
}

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 2019325 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))