Average Error: 58.1 → 0.0
Time: 22.7s
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 r2364226 = x;
        double r2364227 = exp(r2364226);
        double r2364228 = -r2364226;
        double r2364229 = exp(r2364228);
        double r2364230 = r2364227 - r2364229;
        double r2364231 = r2364227 + r2364229;
        double r2364232 = r2364230 / r2364231;
        return r2364232;
}
↓
double f(double x) {
        double r2364233 = x;
        double r2364234 = tanh(r2364233);
        return r2364234;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019158 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))