Average Error: 0.0 → 0.1
Time: 2.0s
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 r284817 = x;
        double r284818 = y;
        double r284819 = 1.0;
        double r284820 = r284817 * r284818;
        double r284821 = 2.0;
        double r284822 = r284820 / r284821;
        double r284823 = r284819 + r284822;
        double r284824 = r284818 / r284823;
        double r284825 = r284817 - r284824;
        return r284825;
}
↓
double f(double x, double y) {
        double r284826 = x;
        double r284827 = y;
        double r284828 = 1.0;
        double r284829 = 2.0;
        double r284830 = r284829 / r284827;
        double r284831 = r284826 / r284830;
        double r284832 = r284828 + r284831;
        double r284833 = r284827 / r284832;
        double r284834 = r284826 - r284833;
        return r284834;
}

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*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))