Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{\frac{x \cdot y}{2} + 1}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{\frac{x \cdot y}{2} + 1}
double f(double x, double y) {
        double r163408 = x;
        double r163409 = y;
        double r163410 = 1.0;
        double r163411 = r163408 * r163409;
        double r163412 = 2.0;
        double r163413 = r163411 / r163412;
        double r163414 = r163410 + r163413;
        double r163415 = r163409 / r163414;
        double r163416 = r163408 - r163415;
        return r163416;
}
↓
double f(double x, double y) {
        double r163417 = x;
        double r163418 = y;
        double r163419 = r163417 * r163418;
        double r163420 = 2.0;
        double r163421 = r163419 / r163420;
        double r163422 = 1.0;
        double r163423 = r163421 + r163422;
        double r163424 = r163418 / r163423;
        double r163425 = r163417 - r163424;
        return r163425;
}

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

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))