Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x \cdot y}{2}}
double f(double x, double y) {
        double r373214 = x;
        double r373215 = y;
        double r373216 = 1.0;
        double r373217 = r373214 * r373215;
        double r373218 = 2.0;
        double r373219 = r373217 / r373218;
        double r373220 = r373216 + r373219;
        double r373221 = r373215 / r373220;
        double r373222 = r373214 - r373221;
        return r373222;
}
↓
double f(double x, double y) {
        double r373223 = x;
        double r373224 = y;
        double r373225 = 1.0;
        double r373226 = r373223 * r373224;
        double r373227 = 2.0;
        double r373228 = r373226 / r373227;
        double r373229 = r373225 + r373228;
        double r373230 = r373224 / r373229;
        double r373231 = r373223 - r373230;
        return r373231;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))