Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 10.6s

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 r40431 = x;
        double r40432 = exp(r40431);
        double r40433 = -r40431;
        double r40434 = exp(r40433);
        double r40435 = r40432 - r40434;
        double r40436 = r40432 + r40434;
        double r40437 = r40435 / r40436;
        return r40437;
}

↓

double f(double x) {
        double r40438 = x;
        double r40439 = tanh(r40438);
        return r40439;
}

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)))))