Average Error: 0.0 → 0.0
Time: 5.3s
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 r136679 = x;
        double r136680 = y;
        double r136681 = 1.0;
        double r136682 = r136679 * r136680;
        double r136683 = 2.0;
        double r136684 = r136682 / r136683;
        double r136685 = r136681 + r136684;
        double r136686 = r136680 / r136685;
        double r136687 = r136679 - r136686;
        return r136687;
}
↓
double f(double x, double y) {
        double r136688 = x;
        double r136689 = y;
        double r136690 = 1.0;
        double r136691 = r136688 * r136689;
        double r136692 = 2.0;
        double r136693 = r136691 / r136692;
        double r136694 = r136690 + r136693;
        double r136695 = r136689 / r136694;
        double r136696 = r136688 - r136695;
        return r136696;
}

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 1978988140 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))