Average Error: 58.3 → 0.0
Time: 31.9s
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 r3747606 = x;
        double r3747607 = exp(r3747606);
        double r3747608 = -r3747606;
        double r3747609 = exp(r3747608);
        double r3747610 = r3747607 - r3747609;
        double r3747611 = r3747607 + r3747609;
        double r3747612 = r3747610 / r3747611;
        return r3747612;
}
↓
double f(double x) {
        double r3747613 = x;
        double r3747614 = tanh(r3747613);
        return r3747614;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.3

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019119 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))