Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H

Average Error: 0.1 → 0.1

Time: 4.3s

Precision: binary64

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

Math

\[\frac{x \cdot x - 3}{6}\]

↓

\[\frac{x \cdot x}{6} - \frac{3}{6}\]

C

double code(double x) {
	return (((double) (((double) (x * x)) - 3.0)) / 6.0);
}

↓

double code(double x) {
	return ((double) ((((double) (x * x)) / 6.0) - (3.0 / 6.0)));
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[\frac{x \cdot x - 3}{6}\]
2. Using strategy rm

3. Applied div-sub 0.1

   \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]

4. Final simplification 0.1

   \[\leadsto \frac{x \cdot x}{6} - \frac{3}{6}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3.0) 6.0))