Average Error: 0.2 → 0.2
Time: 2.6s
Precision: binary64
\[\frac{x \cdot x - 3}{6} \]
↓
\[\frac{x \cdot x - 3}{6} \]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x - 3}{6}

(FPCore (x) :precision binary64 (/ (- (* x x) 3.0) 6.0))
↓
(FPCore (x) :precision binary64 (/ (- (* x x) 3.0) 6.0))
double code(double x) {
	return ((x * x) - 3.0) / 6.0;
}
↓
double code(double x) {
	return ((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 0.2

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

  2. Applied *-un-lft-identity_binary640.2

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

  3. Applied associate-/r*_binary640.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2021280 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3.0) 6.0))