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

Average Error: 0.2 → 0.2

Time: 12.3s

Precision: 64

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

Math

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

↓

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

C

double f(double x) {
        double r78731 = x;
        double r78732 = r78731 * r78731;
        double r78733 = 3.0;
        double r78734 = r78732 - r78733;
        double r78735 = 6.0;
        double r78736 = r78734 / r78735;
        return r78736;
}

↓

double f(double x) {
        double r78737 = x;
        double r78738 = r78737 * r78737;
        double r78739 = 3.0;
        double r78740 = r78738 - r78739;
        double r78741 = 6.0;
        double r78742 = r78740 / r78741;
        return r78742;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))