Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 23.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. x = 8.776596381696226e+279

Math

\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

↓

\[\tanh x\]

C

double f(double x) {
        double r52864 = x;
        double r52865 = exp(r52864);
        double r52866 = -r52864;
        double r52867 = exp(r52866);
        double r52868 = r52865 - r52867;
        double r52869 = r52865 + r52867;
        double r52870 = r52868 / r52869;
        return r52870;
}

↓

double f(double x) {
        double r52871 = x;
        double r52872 = tanh(r52871);
        return r52872;
}

Error

Bits error versus x

Derivation

1. Initial program 58.2

   \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
2. Using strategy rm

3. Applied tanh-undef 0.0

   \[\leadsto \color{blue}{\tanh x}\]

4. Final simplification 0.0

   \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))