Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 14.4s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = 1.3481840315279074e+121

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r52691 = x;
        double r52692 = exp(r52691);
        double r52693 = -r52691;
        double r52694 = exp(r52693);
        double r52695 = r52692 - r52694;
        double r52696 = r52692 + r52694;
        double r52697 = r52695 / r52696;
        return r52697;
}

↓

double f(double x) {
        double r52698 = x;
        double r52699 = tanh(r52698);
        return r52699;
}

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 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))