Average Error: 0.0 → 0.0
Time: 2.2s
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 r190789 = x;
        double r190790 = y;
        double r190791 = 1.0;
        double r190792 = r190789 * r190790;
        double r190793 = 2.0;
        double r190794 = r190792 / r190793;
        double r190795 = r190791 + r190794;
        double r190796 = r190790 / r190795;
        double r190797 = r190789 - r190796;
        return r190797;
}
↓
double f(double x, double y) {
        double r190798 = x;
        double r190799 = y;
        double r190800 = 1.0;
        double r190801 = r190798 * r190799;
        double r190802 = 2.0;
        double r190803 = r190801 / r190802;
        double r190804 = r190800 + r190803;
        double r190805 = r190799 / r190804;
        double r190806 = r190798 - r190805;
        return r190806;
}

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 2020060 +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)))))