Average Error: 0.0 → 0.0
Time: 1.5s
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 r278521 = x;
        double r278522 = y;
        double r278523 = 1.0;
        double r278524 = r278521 * r278522;
        double r278525 = 2.0;
        double r278526 = r278524 / r278525;
        double r278527 = r278523 + r278526;
        double r278528 = r278522 / r278527;
        double r278529 = r278521 - r278528;
        return r278529;
}
↓
double f(double x, double y) {
        double r278530 = x;
        double r278531 = y;
        double r278532 = 1.0;
        double r278533 = r278530 * r278531;
        double r278534 = 2.0;
        double r278535 = r278533 / r278534;
        double r278536 = r278532 + r278535;
        double r278537 = r278531 / r278536;
        double r278538 = r278530 - r278537;
        return r278538;
}

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 2019354 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))