Hyperbolic tangent

Average Error: 58.0 → 0.0

Time: 20.3s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = -1.4028819597761525e+262

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r48800 = x;
        double r48801 = exp(r48800);
        double r48802 = -r48800;
        double r48803 = exp(r48802);
        double r48804 = r48801 - r48803;
        double r48805 = r48801 + r48803;
        double r48806 = r48804 / r48805;
        return r48806;
}

↓

double f(double x) {
        double r48807 = x;
        double r48808 = tanh(r48807);
        return r48808;
}

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