Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 11.3s

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 r82747 = x;
        double r82748 = exp(r82747);
        double r82749 = -r82747;
        double r82750 = exp(r82749);
        double r82751 = r82748 - r82750;
        double r82752 = r82748 + r82750;
        double r82753 = r82751 / r82752;
        return r82753;
}

↓

double f(double x) {
        double r82754 = x;
        double r82755 = tanh(r82754);
        return r82755;
}

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