Average Error: 58.0 → 0.0
Time: 17.7s
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 r1021569 = x;
        double r1021570 = exp(r1021569);
        double r1021571 = -r1021569;
        double r1021572 = exp(r1021571);
        double r1021573 = r1021570 - r1021572;
        double r1021574 = r1021570 + r1021572;
        double r1021575 = r1021573 / r1021574;
        return r1021575;
}
↓
double f(double x) {
        double r1021576 = x;
        double r1021577 = tanh(r1021576);
        return r1021577;
}

Error

Bits error versus x

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Results

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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)))))