Hyperbolic tangent

Average Error: 58.0 → 0.0

Time: 14.8s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = -1.4028819597761525e+262

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r43538 = x;
        double r43539 = exp(r43538);
        double r43540 = -r43538;
        double r43541 = exp(r43540);
        double r43542 = r43539 - r43541;
        double r43543 = r43539 + r43541;
        double r43544 = r43542 / r43543;
        return r43544;
}

↓

double f(double x) {
        double r43545 = x;
        double r43546 = tanh(r43545);
        return r43546;
}

Error

Bits error versus x

Derivation

1. Initial program 58.0

   \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
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 2020046 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))