Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}
(FPCore (x y) :precision binary64 (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))
↓
(FPCore (x y) :precision binary64 (- x (/ y (+ 1.0 (/ x (/ 2.0 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 + (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 associate-/l*_binary64_82070.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021043 
(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)))))