Average Error: 0.0 → 0.0
Time: 10.9s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x \cdot y}{2}}
double f(double x, double y) {
        double r164727 = x;
        double r164728 = y;
        double r164729 = 1.0;
        double r164730 = r164727 * r164728;
        double r164731 = 2.0;
        double r164732 = r164730 / r164731;
        double r164733 = r164729 + r164732;
        double r164734 = r164728 / r164733;
        double r164735 = r164727 - r164734;
        return r164735;
}
↓
double f(double x, double y) {
        double r164736 = x;
        double r164737 = y;
        double r164738 = 1.0;
        double r164739 = r164736 * r164737;
        double r164740 = 2.0;
        double r164741 = r164739 / r164740;
        double r164742 = r164738 + r164741;
        double r164743 = r164737 / r164742;
        double r164744 = r164736 - r164743;
        return r164744;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))