Average Error: 0.0 → 0.1
Time: 5.3s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - y \cdot \frac{1}{1 + \frac{x}{\frac{2}{y}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - y \cdot \frac{1}{1 + \frac{x}{\frac{2}{y}}}
double code(double x, double y) {
	return (x - (y / (1.0 + ((x * y) / 2.0))));
}
↓
double code(double x, double y) {
	return (x - (y * (1.0 / (1.0 + (x / (2.0 / y))))));
}

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 div-inv0.1

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

  5. Applied associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 +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)))))