Average Error: 58.2 → 0.0
Time: 24.6s
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 r25118 = x;
        double r25119 = exp(r25118);
        double r25120 = -r25118;
        double r25121 = exp(r25120);
        double r25122 = r25119 - r25121;
        double r25123 = r25119 + r25121;
        double r25124 = r25122 / r25123;
        return r25124;
}
↓
double f(double x) {
        double r25125 = x;
        double r25126 = tanh(r25125);
        return r25126;
}

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 2019235 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))