Average Error: 58.1 → 0.0
Time: 18.2s
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 r2476402 = x;
        double r2476403 = exp(r2476402);
        double r2476404 = -r2476402;
        double r2476405 = exp(r2476404);
        double r2476406 = r2476403 - r2476405;
        double r2476407 = r2476403 + r2476405;
        double r2476408 = r2476406 / r2476407;
        return r2476408;
}
↓
double f(double x) {
        double r2476409 = x;
        double r2476410 = tanh(r2476409);
        return r2476410;
}

Error

Bits error versus x

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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 2019138 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))