Hyperbolic tangent

Average Error: 58.2 → 0.0

Time: 13.3s

Precision: 64

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

• could not determine a ground truth for program body

  1. x = 3.3915171398033327e+295

Math

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

↓

\[\tanh x\]

C

double f(double x) {
        double r62736 = x;
        double r62737 = exp(r62736);
        double r62738 = -r62736;
        double r62739 = exp(r62738);
        double r62740 = r62737 - r62739;
        double r62741 = r62737 + r62739;
        double r62742 = r62740 / r62741;
        return r62742;
}

↓

double f(double x) {
        double r62743 = x;
        double r62744 = tanh(r62743);
        return r62744;
}

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)))))