Average Error: 0.1 → 0.1
Time: 2.8s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{\mathsf{fma}\left(x, x, -3\right)}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{\mathsf{fma}\left(x, x, -3\right)}{6}
double code(double x) {
	return (((x * x) - 3.0) / 6.0);
}
↓
double code(double x) {
	return (fma(x, x, -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 0.1

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

  3. Applied fma-neg0.1

    \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -3\right)}}{6}\]

  4. Final simplification0.1

    \[\leadsto \frac{\mathsf{fma}\left(x, x, -3\right)}{6}\]

Reproduce

herbie shell --seed 2020075 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))