Average Error: 0.0 → 0.1
Time: 1.9s
Precision: binary64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x + \frac{-1}{\frac{x}{2} + \frac{1}{y}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x + \frac{-1}{\frac{x}{2} + \frac{1}{y}}
(FPCore (x y) :precision binary64 (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))
↓
(FPCore (x y) :precision binary64 (+ x (/ -1.0 (+ (/ x 2.0) (/ 1.0 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) ((x / 2.0) + (1.0 / 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 Error: 0.0 bits

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

  2. SimplifiedError: 0.1 bits

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

  3. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020203 
(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)))))