Average Error: 58.1 → 0.0
Time: 15.8s
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 r1368975 = x;
        double r1368976 = exp(r1368975);
        double r1368977 = -r1368975;
        double r1368978 = exp(r1368977);
        double r1368979 = r1368976 - r1368978;
        double r1368980 = r1368976 + r1368978;
        double r1368981 = r1368979 / r1368980;
        return r1368981;
}
↓
double f(double x) {
        double r1368982 = x;
        double r1368983 = tanh(r1368982);
        return r1368983;
}

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 2019138 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))