Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 14.0s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = 1.3481840315279074e+121

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r50492 = x;
        double r50493 = exp(r50492);
        double r50494 = -r50492;
        double r50495 = exp(r50494);
        double r50496 = r50493 - r50495;
        double r50497 = r50493 + r50495;
        double r50498 = r50496 / r50497;
        return r50498;
}

↓

double f(double x) {
        double r50499 = x;
        double r50500 = tanh(r50499);
        return r50500;
}

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 2019350 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))