Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 12.3s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = -8.55741656464672e+51

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r50356 = x;
        double r50357 = exp(r50356);
        double r50358 = -r50356;
        double r50359 = exp(r50358);
        double r50360 = r50357 - r50359;
        double r50361 = r50357 + r50359;
        double r50362 = r50360 / r50361;
        return r50362;
}

↓

double f(double x) {
        double r50363 = x;
        double r50364 = tanh(r50363);
        return r50364;
}

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 2019351 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))