Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 10.3s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = -2.9618829731577474e+29

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r53755 = x;
        double r53756 = exp(r53755);
        double r53757 = -r53755;
        double r53758 = exp(r53757);
        double r53759 = r53756 - r53758;
        double r53760 = r53756 + r53758;
        double r53761 = r53759 / r53760;
        return r53761;
}

↓

double f(double x) {
        double r53762 = x;
        double r53763 = tanh(r53762);
        return r53763;
}

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 2020042 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))