Average Error: 0.0 → 0.0
Time: 1.8s
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 r255666 = x;
        double r255667 = y;
        double r255668 = 1.0;
        double r255669 = r255666 * r255667;
        double r255670 = 2.0;
        double r255671 = r255669 / r255670;
        double r255672 = r255668 + r255671;
        double r255673 = r255667 / r255672;
        double r255674 = r255666 - r255673;
        return r255674;
}
↓
double f(double x, double y) {
        double r255675 = x;
        double r255676 = y;
        double r255677 = 1.0;
        double r255678 = r255675 * r255676;
        double r255679 = 2.0;
        double r255680 = r255678 / r255679;
        double r255681 = r255677 + r255680;
        double r255682 = r255676 / r255681;
        double r255683 = r255675 - r255682;
        return r255683;
}

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 2020034 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))