Average Error: 0.0 → 0.0
Time: 3.2s
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 r204814 = x;
        double r204815 = y;
        double r204816 = 1.0;
        double r204817 = r204814 * r204815;
        double r204818 = 2.0;
        double r204819 = r204817 / r204818;
        double r204820 = r204816 + r204819;
        double r204821 = r204815 / r204820;
        double r204822 = r204814 - r204821;
        return r204822;
}
↓
double f(double x, double y) {
        double r204823 = x;
        double r204824 = y;
        double r204825 = 1.0;
        double r204826 = r204823 * r204824;
        double r204827 = 2.0;
        double r204828 = r204826 / r204827;
        double r204829 = r204825 + r204828;
        double r204830 = r204824 / r204829;
        double r204831 = r204823 - r204830;
        return r204831;
}

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 +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)))))