Average Error: 58.2 → 0.0
Time: 1.1m
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 r1657375 = x;
        double r1657376 = exp(r1657375);
        double r1657377 = -r1657375;
        double r1657378 = exp(r1657377);
        double r1657379 = r1657376 - r1657378;
        double r1657380 = r1657376 + r1657378;
        double r1657381 = r1657379 / r1657380;
        return r1657381;
}
↓
double f(double x) {
        double r1657382 = x;
        double r1657383 = tanh(r1657382);
        return r1657383;
}

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 2019192 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))