Average Error: 0.0 → 0.0
Time: 9.3s
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 r150338 = x;
        double r150339 = y;
        double r150340 = 1.0;
        double r150341 = r150338 * r150339;
        double r150342 = 2.0;
        double r150343 = r150341 / r150342;
        double r150344 = r150340 + r150343;
        double r150345 = r150339 / r150344;
        double r150346 = r150338 - r150345;
        return r150346;
}
↓
double f(double x, double y) {
        double r150347 = x;
        double r150348 = y;
        double r150349 = 1.0;
        double r150350 = r150347 * r150348;
        double r150351 = 2.0;
        double r150352 = r150350 / r150351;
        double r150353 = r150349 + r150352;
        double r150354 = r150348 / r150353;
        double r150355 = r150347 - r150354;
        return r150355;
}

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 2019294 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))