Average Error: 0.2 → 0.1
Time: 1.3s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{-6} \cdot \left(-x\right) - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{-6} \cdot \left(-x\right) - \frac{3}{6}
double code(double x) {
	return ((double) (((double) (((double) (x * x)) - 3.0)) / 6.0));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (x / ((double) -(6.0)))) * ((double) -(x)))) - ((double) (3.0 / 6.0))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  3. Applied div-sub0.2

    \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.2

    \[\leadsto \frac{x \cdot \color{blue}{\left(1 \cdot x\right)}}{6} - \frac{3}{6}\]

  6. Applied associate-*r*0.2

    \[\leadsto \frac{\color{blue}{\left(x \cdot 1\right) \cdot x}}{6} - \frac{3}{6}\]

  7. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x \cdot 1}{\frac{6}{x}}} - \frac{3}{6}\]
  8. Using strategy rm

  9. Applied frac-2neg0.1

    \[\leadsto \frac{x \cdot 1}{\color{blue}{\frac{-6}{-x}}} - \frac{3}{6}\]

  10. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{x \cdot 1}{-6} \cdot \left(-x\right)} - \frac{3}{6}\]

  11. Simplified0.1

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

  12. Final simplification0.1

    \[\leadsto \frac{x}{-6} \cdot \left(-x\right) - \frac{3}{6}\]

Reproduce

herbie shell --seed 2020114 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))