Average Error: 0.0 → 0.1
Time: 30.1s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{1}{\frac{\frac{y \cdot x}{2} + 1}{y}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{1}{\frac{\frac{y \cdot x}{2} + 1}{y}}
double f(double x, double y) {
        double r12446663 = x;
        double r12446664 = y;
        double r12446665 = 1.0;
        double r12446666 = r12446663 * r12446664;
        double r12446667 = 2.0;
        double r12446668 = r12446666 / r12446667;
        double r12446669 = r12446665 + r12446668;
        double r12446670 = r12446664 / r12446669;
        double r12446671 = r12446663 - r12446670;
        return r12446671;
}
↓
double f(double x, double y) {
        double r12446672 = x;
        double r12446673 = 1.0;
        double r12446674 = y;
        double r12446675 = r12446674 * r12446672;
        double r12446676 = 2.0;
        double r12446677 = r12446675 / r12446676;
        double r12446678 = 1.0;
        double r12446679 = r12446677 + r12446678;
        double r12446680 = r12446679 / r12446674;
        double r12446681 = r12446673 / r12446680;
        double r12446682 = r12446672 - r12446681;
        return r12446682;
}

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. Using strategy rm

  3. Applied clear-num0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))