Average Error: 0.0 → 0.0
Time: 1.4s
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 r184496 = x;
        double r184497 = y;
        double r184498 = 1.0;
        double r184499 = r184496 * r184497;
        double r184500 = 2.0;
        double r184501 = r184499 / r184500;
        double r184502 = r184498 + r184501;
        double r184503 = r184497 / r184502;
        double r184504 = r184496 - r184503;
        return r184504;
}
↓
double f(double x, double y) {
        double r184505 = x;
        double r184506 = y;
        double r184507 = 1.0;
        double r184508 = r184505 * r184506;
        double r184509 = 2.0;
        double r184510 = r184508 / r184509;
        double r184511 = r184507 + r184510;
        double r184512 = r184506 / r184511;
        double r184513 = r184505 - r184512;
        return r184513;
}

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 2019356 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))