Average Error: 0.0 → 0.0
Time: 1.9s
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 r243708 = x;
        double r243709 = y;
        double r243710 = 1.0;
        double r243711 = r243708 * r243709;
        double r243712 = 2.0;
        double r243713 = r243711 / r243712;
        double r243714 = r243710 + r243713;
        double r243715 = r243709 / r243714;
        double r243716 = r243708 - r243715;
        return r243716;
}
↓
double f(double x, double y) {
        double r243717 = x;
        double r243718 = y;
        double r243719 = 1.0;
        double r243720 = r243717 * r243718;
        double r243721 = 2.0;
        double r243722 = r243720 / r243721;
        double r243723 = r243719 + r243722;
        double r243724 = r243718 / r243723;
        double r243725 = r243717 - r243724;
        return r243725;
}

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 2020024 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))