Average Error: 58.2 → 0.0
Time: 24.4s
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 r48268 = x;
        double r48269 = exp(r48268);
        double r48270 = -r48268;
        double r48271 = exp(r48270);
        double r48272 = r48269 - r48271;
        double r48273 = r48269 + r48271;
        double r48274 = r48272 / r48273;
        return r48274;
}
↓
double f(double x) {
        double r48275 = x;
        double r48276 = tanh(r48275);
        return r48276;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))