Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 19.7s

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 r34301 = x;
        double r34302 = exp(r34301);
        double r34303 = -r34301;
        double r34304 = exp(r34303);
        double r34305 = r34302 - r34304;
        double r34306 = r34302 + r34304;
        double r34307 = r34305 / r34306;
        return r34307;
}

↓

double f(double x) {
        double r34308 = x;
        double r34309 = tanh(r34308);
        return r34309;
}

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