Average Error: 0.0 → 0.0
Time: 1.6s
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 r223678 = x;
        double r223679 = y;
        double r223680 = 1.0;
        double r223681 = r223678 * r223679;
        double r223682 = 2.0;
        double r223683 = r223681 / r223682;
        double r223684 = r223680 + r223683;
        double r223685 = r223679 / r223684;
        double r223686 = r223678 - r223685;
        return r223686;
}
↓
double f(double x, double y) {
        double r223687 = x;
        double r223688 = y;
        double r223689 = 1.0;
        double r223690 = r223687 * r223688;
        double r223691 = 2.0;
        double r223692 = r223690 / r223691;
        double r223693 = r223689 + r223692;
        double r223694 = r223688 / r223693;
        double r223695 = r223687 - r223694;
        return r223695;
}

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 2019354 +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)))))