Average Error: 58.1 → 0.0
Time: 18.9s
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 r44957 = x;
        double r44958 = exp(r44957);
        double r44959 = -r44957;
        double r44960 = exp(r44959);
        double r44961 = r44958 - r44960;
        double r44962 = r44958 + r44960;
        double r44963 = r44961 / r44962;
        return r44963;
}
↓
double f(double x) {
        double r44964 = x;
        double r44965 = tanh(r44964);
        return r44965;
}

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 2019303 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))