Average Error: 0.1 → 0.1
Time: 1.0s
Precision: binary64
\[\frac{x \cdot x - 3}{6}\]
↓
\[x \cdot \frac{x}{6} - 0.5\]
\frac{x \cdot x - 3}{6}
↓
x \cdot \frac{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. Using strategy rm

  6. Applied *-un-lft-identity_binary640.1

    \[\leadsto \frac{x \cdot x}{\color{blue}{1 \cdot 6}} - 0.5\]

  7. Applied times-frac_binary640.1

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{x}{6}} - 0.5\]

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020231 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3.0) 6.0))