Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{y}{\frac{2}{x}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{y}{\frac{2}{x}}}
double code(double x, double y) {
	return ((double) (x - ((double) (y / ((double) (1.0 + ((double) (((double) (x * y)) / 2.0))))))));
}
↓
double code(double x, double y) {
	return ((double) (x - ((double) (y / ((double) (1.0 + ((double) (y / ((double) (2.0 / x))))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
  2. Using strategy rm

  3. Applied *-commutative0.0

    \[\leadsto x - \frac{y}{1 + \frac{\color{blue}{y \cdot x}}{2}}\]

  4. Applied associate-/l*0.0

    \[\leadsto x - \frac{y}{1 + \color{blue}{\frac{y}{\frac{2}{x}}}}\]

  5. Final simplification0.0

    \[\leadsto x - \frac{y}{1 + \frac{y}{\frac{2}{x}}}\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))