Average Error: 58.1 → 0.0
Time: 18.4s
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 r2294324 = x;
        double r2294325 = exp(r2294324);
        double r2294326 = -r2294324;
        double r2294327 = exp(r2294326);
        double r2294328 = r2294325 - r2294327;
        double r2294329 = r2294325 + r2294327;
        double r2294330 = r2294328 / r2294329;
        return r2294330;
}
↓
double f(double x) {
        double r2294331 = x;
        double r2294332 = tanh(r2294331);
        return r2294332;
}

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 2019164 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))