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 = 8.776596381696226e+279

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r55443 = x;
        double r55444 = exp(r55443);
        double r55445 = -r55443;
        double r55446 = exp(r55445);
        double r55447 = r55444 - r55446;
        double r55448 = r55444 + r55446;
        double r55449 = r55447 / r55448;
        return r55449;
}

↓

double f(double x) {
        double r55450 = x;
        double r55451 = tanh(r55450);
        return r55451;
}

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 2020045 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))