Average Error: 0.0 → 0.0
Time: 3.0s
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 r194806 = x;
        double r194807 = y;
        double r194808 = 1.0;
        double r194809 = r194806 * r194807;
        double r194810 = 2.0;
        double r194811 = r194809 / r194810;
        double r194812 = r194808 + r194811;
        double r194813 = r194807 / r194812;
        double r194814 = r194806 - r194813;
        return r194814;
}
↓
double f(double x, double y) {
        double r194815 = x;
        double r194816 = y;
        double r194817 = 1.0;
        double r194818 = 2.0;
        double r194819 = r194818 / r194816;
        double r194820 = r194815 / r194819;
        double r194821 = r194817 + r194820;
        double r194822 = r194816 / r194821;
        double r194823 = r194815 - r194822;
        return r194823;
}

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 2020001 +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)))))