Average Error: 58.2 → 0.0
Time: 23.4s
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 r43617 = x;
        double r43618 = exp(r43617);
        double r43619 = -r43617;
        double r43620 = exp(r43619);
        double r43621 = r43618 - r43620;
        double r43622 = r43618 + r43620;
        double r43623 = r43621 / r43622;
        return r43623;
}
↓
double f(double x) {
        double r43624 = x;
        double r43625 = tanh(r43624);
        return r43625;
}

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 2019326 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))