Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{\frac{x \cdot y}{2} + 1}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{\frac{x \cdot y}{2} + 1}
double f(double x, double y) {
        double r195645 = x;
        double r195646 = y;
        double r195647 = 1.0;
        double r195648 = r195645 * r195646;
        double r195649 = 2.0;
        double r195650 = r195648 / r195649;
        double r195651 = r195647 + r195650;
        double r195652 = r195646 / r195651;
        double r195653 = r195645 - r195652;
        return r195653;
}
↓
double f(double x, double y) {
        double r195654 = x;
        double r195655 = y;
        double r195656 = r195654 * r195655;
        double r195657 = 2.0;
        double r195658 = r195656 / r195657;
        double r195659 = 1.0;
        double r195660 = r195658 + r195659;
        double r195661 = r195655 / r195660;
        double r195662 = r195654 - r195661;
        return r195662;
}

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

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))