Average Error: 0.0 → 0.0
Time: 3.0s
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 r222608 = x;
        double r222609 = y;
        double r222610 = 1.0;
        double r222611 = r222608 * r222609;
        double r222612 = 2.0;
        double r222613 = r222611 / r222612;
        double r222614 = r222610 + r222613;
        double r222615 = r222609 / r222614;
        double r222616 = r222608 - r222615;
        return r222616;
}
↓
double f(double x, double y) {
        double r222617 = x;
        double r222618 = y;
        double r222619 = 1.0;
        double r222620 = r222617 * r222618;
        double r222621 = 2.0;
        double r222622 = r222620 / r222621;
        double r222623 = r222619 + r222622;
        double r222624 = r222618 / r222623;
        double r222625 = r222617 - r222624;
        return r222625;
}

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 2020002 +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)))))