Average Error: 0.0 → 0.0
Time: 10.3s
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 r157573 = x;
        double r157574 = y;
        double r157575 = 1.0;
        double r157576 = r157573 * r157574;
        double r157577 = 2.0;
        double r157578 = r157576 / r157577;
        double r157579 = r157575 + r157578;
        double r157580 = r157574 / r157579;
        double r157581 = r157573 - r157580;
        return r157581;
}
↓
double f(double x, double y) {
        double r157582 = x;
        double r157583 = y;
        double r157584 = 1.0;
        double r157585 = r157582 * r157583;
        double r157586 = 2.0;
        double r157587 = r157585 / r157586;
        double r157588 = r157584 + r157587;
        double r157589 = r157583 / r157588;
        double r157590 = r157582 - r157589;
        return r157590;
}

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)))))