Average Error: 0.0 → 0.0
Time: 3.6s
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 r214708 = x;
        double r214709 = y;
        double r214710 = 1.0;
        double r214711 = r214708 * r214709;
        double r214712 = 2.0;
        double r214713 = r214711 / r214712;
        double r214714 = r214710 + r214713;
        double r214715 = r214709 / r214714;
        double r214716 = r214708 - r214715;
        return r214716;
}
↓
double f(double x, double y) {
        double r214717 = x;
        double r214718 = y;
        double r214719 = 1.0;
        double r214720 = r214717 * r214718;
        double r214721 = 2.0;
        double r214722 = r214720 / r214721;
        double r214723 = r214719 + r214722;
        double r214724 = r214718 / r214723;
        double r214725 = r214717 - r214724;
        return r214725;
}

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 2020062 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))