Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 10.3s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = 3.3915171398033327e+295

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r44815 = x;
        double r44816 = exp(r44815);
        double r44817 = -r44815;
        double r44818 = exp(r44817);
        double r44819 = r44816 - r44818;
        double r44820 = r44816 + r44818;
        double r44821 = r44819 / r44820;
        return r44821;
}

↓

double f(double x) {
        double r44822 = x;
        double r44823 = tanh(r44822);
        return r44823;
}

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 2020047 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))