Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[x - \frac{y}{1.0 + \frac{x \cdot y}{2.0}}\]
↓
\[x - \frac{y}{\frac{x \cdot y}{2.0} + 1.0}\]
x - \frac{y}{1.0 + \frac{x \cdot y}{2.0}}
↓
x - \frac{y}{\frac{x \cdot y}{2.0} + 1.0}
double f(double x, double y) {
        double r12664867 = x;
        double r12664868 = y;
        double r12664869 = 1.0;
        double r12664870 = r12664867 * r12664868;
        double r12664871 = 2.0;
        double r12664872 = r12664870 / r12664871;
        double r12664873 = r12664869 + r12664872;
        double r12664874 = r12664868 / r12664873;
        double r12664875 = r12664867 - r12664874;
        return r12664875;
}
↓
double f(double x, double y) {
        double r12664876 = x;
        double r12664877 = y;
        double r12664878 = r12664876 * r12664877;
        double r12664879 = 2.0;
        double r12664880 = r12664878 / r12664879;
        double r12664881 = 1.0;
        double r12664882 = r12664880 + r12664881;
        double r12664883 = r12664877 / r12664882;
        double r12664884 = r12664876 - r12664883;
        return r12664884;
}

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

    \[x - \frac{y}{1.0 + \frac{x \cdot y}{2.0}}\]

  2. Final simplification0.0

    \[\leadsto x - \frac{y}{\frac{x \cdot y}{2.0} + 1.0}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))