Average Error: 0.0 → 0.0
Time: 1.5s
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 r205671 = x;
        double r205672 = y;
        double r205673 = 1.0;
        double r205674 = r205671 * r205672;
        double r205675 = 2.0;
        double r205676 = r205674 / r205675;
        double r205677 = r205673 + r205676;
        double r205678 = r205672 / r205677;
        double r205679 = r205671 - r205678;
        return r205679;
}
↓
double f(double x, double y) {
        double r205680 = x;
        double r205681 = y;
        double r205682 = 1.0;
        double r205683 = r205680 * r205681;
        double r205684 = 2.0;
        double r205685 = r205683 / r205684;
        double r205686 = r205682 + r205685;
        double r205687 = r205681 / r205686;
        double r205688 = r205680 - r205687;
        return r205688;
}

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 2020018 +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)))))