Average Error: 0.1 → 0.1
Time: 893.0ms
Precision: binary64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x}{6} - 0.5\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x}{6} - 0.5
(FPCore (x) :precision binary64 (/ (- (* x x) 3.0) 6.0))
↓
(FPCore (x) :precision binary64 (- (/ (* x x) 6.0) 0.5))
double code(double x) {
	return ((x * x) - 3.0) / 6.0;
}
↓
double code(double x) {
	return ((x * x) / 6.0) - 0.5;
}

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 div-sub_binary640.1

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

  4. Simplified0.1

    \[\leadsto \frac{x \cdot x}{6} - \color{blue}{0.5}\]

  5. Final simplification0.1

    \[\leadsto \frac{x \cdot x}{6} - 0.5\]

Reproduce

herbie shell --seed 2020224 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3.0) 6.0))