Average Error: 0.0 → 0.0
Time: 2.0s
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 r350645 = x;
        double r350646 = y;
        double r350647 = 1.0;
        double r350648 = r350645 * r350646;
        double r350649 = 2.0;
        double r350650 = r350648 / r350649;
        double r350651 = r350647 + r350650;
        double r350652 = r350646 / r350651;
        double r350653 = r350645 - r350652;
        return r350653;
}
↓
double f(double x, double y) {
        double r350654 = x;
        double r350655 = y;
        double r350656 = 1.0;
        double r350657 = r350654 * r350655;
        double r350658 = 2.0;
        double r350659 = r350657 / r350658;
        double r350660 = r350656 + r350659;
        double r350661 = r350655 / r350660;
        double r350662 = r350654 - r350661;
        return r350662;
}

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 2020065 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))