Average Error: 58.1 → 0.0
Time: 21.6s
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 r36074 = x;
        double r36075 = exp(r36074);
        double r36076 = -r36074;
        double r36077 = exp(r36076);
        double r36078 = r36075 - r36077;
        double r36079 = r36075 + r36077;
        double r36080 = r36078 / r36079;
        return r36080;
}
↓
double f(double x) {
        double r36081 = x;
        double r36082 = tanh(r36081);
        return r36082;
}

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 2019303 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))