Average Error: 58.2 → 0.0
Time: 23.3s
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 r3094550 = x;
        double r3094551 = exp(r3094550);
        double r3094552 = -r3094550;
        double r3094553 = exp(r3094552);
        double r3094554 = r3094551 - r3094553;
        double r3094555 = r3094551 + r3094553;
        double r3094556 = r3094554 / r3094555;
        return r3094556;
}
↓
double f(double x) {
        double r3094557 = x;
        double r3094558 = tanh(r3094557);
        return r3094558;
}

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 2019179 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))