Average Error: 0.0 → 0.1
Time: 2.3s
Precision: binary64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{1}{\frac{1 + \frac{x \cdot y}{2}}{y}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{1}{\frac{1 + \frac{x \cdot y}{2}}{y}}
(FPCore (x y) :precision binary64 (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))
↓
(FPCore (x y) :precision binary64 (- x (/ 1.0 (/ (+ 1.0 (/ (* x y) 2.0)) y))))
double code(double x, double y) {
	return ((double) (x - (y / ((double) (1.0 + (((double) (x * y)) / 2.0))))));
}
↓
double code(double x, double y) {
	return ((double) (x - (1.0 / (((double) (1.0 + (((double) (x * y)) / 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 clear-num_binary640.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020205 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))