Average Error: 0.2 → 0.1
Time: 1.7s
Precision: binary64
\[\frac{x \cdot x - 3}{6}\]
↓
\[x \cdot \frac{x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
x \cdot \frac{x}{6} - \frac{3}{6}
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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.2 bits

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

  3. Applied div-subError: 0.2 bits

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

  4. SimplifiedError: 0.1 bits

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

  5. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020200 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3.0) 6.0))