Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 23.4s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = 3.3915171398033327e+295

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r61416 = x;
        double r61417 = exp(r61416);
        double r61418 = -r61416;
        double r61419 = exp(r61418);
        double r61420 = r61417 - r61419;
        double r61421 = r61417 + r61419;
        double r61422 = r61420 / r61421;
        return r61422;
}

↓

double f(double x) {
        double r61423 = x;
        double r61424 = tanh(r61423);
        return r61424;
}

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)))))