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 r204806 = x;
        double r204807 = y;
        double r204808 = 1.0;
        double r204809 = r204806 * r204807;
        double r204810 = 2.0;
        double r204811 = r204809 / r204810;
        double r204812 = r204808 + r204811;
        double r204813 = r204807 / r204812;
        double r204814 = r204806 - r204813;
        return r204814;
}
↓
double f(double x, double y) {
        double r204815 = x;
        double r204816 = y;
        double r204817 = 1.0;
        double r204818 = 2.0;
        double r204819 = r204818 / r204816;
        double r204820 = r204815 / r204819;
        double r204821 = r204817 + r204820;
        double r204822 = r204816 / r204821;
        double r204823 = r204815 - r204822;
        return r204823;
}

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)))))