Average Error: 58.0 → 0.0
Time: 33.5s
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 r2548361 = x;
        double r2548362 = exp(r2548361);
        double r2548363 = -r2548361;
        double r2548364 = exp(r2548363);
        double r2548365 = r2548362 - r2548364;
        double r2548366 = r2548362 + r2548364;
        double r2548367 = r2548365 / r2548366;
        return r2548367;
}
↓
double f(double x) {
        double r2548368 = x;
        double r2548369 = tanh(r2548368);
        return r2548369;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019151 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))