Average Error: 0.0 → 0.1
Time: 3.2s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}
double f(double x, double y) {
        double r259784 = x;
        double r259785 = y;
        double r259786 = 1.0;
        double r259787 = r259784 * r259785;
        double r259788 = 2.0;
        double r259789 = r259787 / r259788;
        double r259790 = r259786 + r259789;
        double r259791 = r259785 / r259790;
        double r259792 = r259784 - r259791;
        return r259792;
}
↓
double f(double x, double y) {
        double r259793 = x;
        double r259794 = y;
        double r259795 = 1.0;
        double r259796 = 1.0;
        double r259797 = r259793 * r259794;
        double r259798 = 2.0;
        double r259799 = r259797 / r259798;
        double r259800 = r259796 + r259799;
        double r259801 = r259795 / r259800;
        double r259802 = r259794 * r259801;
        double r259803 = r259793 - r259802;
        return r259803;
}

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. Using strategy rm

  3. Applied div-inv0.1

    \[\leadsto x - \color{blue}{y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}}\]

  4. Final simplification0.1

    \[\leadsto x - y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}\]

Reproduce

herbie shell --seed 2020046 +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)))))