Average Error: 58.2 → 0.0
Time: 1.8m
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 r21356155 = x;
        double r21356156 = exp(r21356155);
        double r21356157 = -r21356155;
        double r21356158 = exp(r21356157);
        double r21356159 = r21356156 - r21356158;
        double r21356160 = r21356156 + r21356158;
        double r21356161 = r21356159 / r21356160;
        return r21356161;
}
↓
double f(double x) {
        double r21356162 = x;
        double r21356163 = tanh(r21356162);
        return r21356163;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019121 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))