Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 11.5s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = 3.3915171398033327e+295

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r32140 = x;
        double r32141 = exp(r32140);
        double r32142 = -r32140;
        double r32143 = exp(r32142);
        double r32144 = r32141 - r32143;
        double r32145 = r32141 + r32143;
        double r32146 = r32144 / r32145;
        return r32146;
}

↓

double f(double x) {
        double r32147 = x;
        double r32148 = tanh(r32147);
        return r32148;
}

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 2020047 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))