Average Error: 0.0 → 0.0
Time: 2.8s
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 r214680 = x;
        double r214681 = y;
        double r214682 = 1.0;
        double r214683 = r214680 * r214681;
        double r214684 = 2.0;
        double r214685 = r214683 / r214684;
        double r214686 = r214682 + r214685;
        double r214687 = r214681 / r214686;
        double r214688 = r214680 - r214687;
        return r214688;
}
↓
double f(double x, double y) {
        double r214689 = x;
        double r214690 = y;
        double r214691 = 1.0;
        double r214692 = r214689 * r214690;
        double r214693 = 2.0;
        double r214694 = r214692 / r214693;
        double r214695 = r214691 + r214694;
        double r214696 = r214690 / r214695;
        double r214697 = r214689 - r214696;
        return r214697;
}

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 2020062 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))