Average Error: 58.1 → 0.0
Time: 18.9s
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 r1013495 = x;
        double r1013496 = exp(r1013495);
        double r1013497 = -r1013495;
        double r1013498 = exp(r1013497);
        double r1013499 = r1013496 - r1013498;
        double r1013500 = r1013496 + r1013498;
        double r1013501 = r1013499 / r1013500;
        return r1013501;
}
↓
double f(double x) {
        double r1013502 = x;
        double r1013503 = tanh(r1013502);
        return r1013503;
}

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 2019155 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))