Average Error: 58.2 → 0.0
Time: 1.8m
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 r13986357 = x;
        double r13986358 = exp(r13986357);
        double r13986359 = -r13986357;
        double r13986360 = exp(r13986359);
        double r13986361 = r13986358 - r13986360;
        double r13986362 = r13986358 + r13986360;
        double r13986363 = r13986361 / r13986362;
        return r13986363;
}
↓
double f(double x) {
        double r13986364 = x;
        double r13986365 = tanh(r13986364);
        return r13986365;
}

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 2019121 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))