Average Error: 0.0 → 0.0
Time: 2.3s
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 r222354 = x;
        double r222355 = y;
        double r222356 = 1.0;
        double r222357 = r222354 * r222355;
        double r222358 = 2.0;
        double r222359 = r222357 / r222358;
        double r222360 = r222356 + r222359;
        double r222361 = r222355 / r222360;
        double r222362 = r222354 - r222361;
        return r222362;
}
↓
double f(double x, double y) {
        double r222363 = x;
        double r222364 = y;
        double r222365 = 1.0;
        double r222366 = r222363 * r222364;
        double r222367 = 2.0;
        double r222368 = r222366 / r222367;
        double r222369 = r222365 + r222368;
        double r222370 = r222364 / r222369;
        double r222371 = r222363 - r222370;
        return r222371;
}

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 2020089 +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)))))