Average Error: 57.9 → 0.0
Time: 21.7s
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 r4248055 = x;
        double r4248056 = exp(r4248055);
        double r4248057 = -r4248055;
        double r4248058 = exp(r4248057);
        double r4248059 = r4248056 - r4248058;
        double r4248060 = r4248056 + r4248058;
        double r4248061 = r4248059 / r4248060;
        return r4248061;
}
↓
double f(double x) {
        double r4248062 = x;
        double r4248063 = tanh(r4248062);
        return r4248063;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 57.9

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019107 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))