Average Error: 58.2 → 0.0
Time: 3.3s
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 r28986 = x;
        double r28987 = exp(r28986);
        double r28988 = -r28986;
        double r28989 = exp(r28988);
        double r28990 = r28987 - r28989;
        double r28991 = r28987 + r28989;
        double r28992 = r28990 / r28991;
        return r28992;
}
↓
double f(double x) {
        double r28993 = x;
        double r28994 = tanh(r28993);
        return r28994;
}

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 2020083 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))