Average Error: 58.0 → 0.0
Time: 17.3s
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 r1023572 = x;
        double r1023573 = exp(r1023572);
        double r1023574 = -r1023572;
        double r1023575 = exp(r1023574);
        double r1023576 = r1023573 - r1023575;
        double r1023577 = r1023573 + r1023575;
        double r1023578 = r1023576 / r1023577;
        return r1023578;
}
↓
double f(double x) {
        double r1023579 = x;
        double r1023580 = tanh(r1023579);
        return r1023580;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019151 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))