Average Error: 58.1 → 0.0
Time: 4.9s
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 r57663 = x;
        double r57664 = exp(r57663);
        double r57665 = -r57663;
        double r57666 = exp(r57665);
        double r57667 = r57664 - r57666;
        double r57668 = r57664 + r57666;
        double r57669 = r57667 / r57668;
        return r57669;
}
↓
double f(double x) {
        double r57670 = x;
        double r57671 = tanh(r57670);
        return r57671;
}

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 2020062 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))