Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}
double f(double x, double y) {
        double r307763 = x;
        double r307764 = y;
        double r307765 = 1.0;
        double r307766 = r307763 * r307764;
        double r307767 = 2.0;
        double r307768 = r307766 / r307767;
        double r307769 = r307765 + r307768;
        double r307770 = r307764 / r307769;
        double r307771 = r307763 - r307770;
        return r307771;
}
↓
double f(double x, double y) {
        double r307772 = x;
        double r307773 = y;
        double r307774 = 1.0;
        double r307775 = 2.0;
        double r307776 = r307775 / r307773;
        double r307777 = r307772 / r307776;
        double r307778 = r307774 + r307777;
        double r307779 = r307773 / r307778;
        double r307780 = r307772 - r307779;
        return r307780;
}

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 associate-/l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))