Average Error: 58.1 → 0.0
Time: 40.1s
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 r2350215 = x;
        double r2350216 = exp(r2350215);
        double r2350217 = -r2350215;
        double r2350218 = exp(r2350217);
        double r2350219 = r2350216 - r2350218;
        double r2350220 = r2350216 + r2350218;
        double r2350221 = r2350219 / r2350220;
        return r2350221;
}
↓
double f(double x) {
        double r2350222 = x;
        double r2350223 = tanh(r2350222);
        return r2350223;
}

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 2019144 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))