Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 11.2s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = -8.55741656464672e+51

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r32299 = x;
        double r32300 = exp(r32299);
        double r32301 = -r32299;
        double r32302 = exp(r32301);
        double r32303 = r32300 - r32302;
        double r32304 = r32300 + r32302;
        double r32305 = r32303 / r32304;
        return r32305;
}

↓

double f(double x) {
        double r32306 = x;
        double r32307 = tanh(r32306);
        return r32307;
}

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 2019351 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))