Average Error: 0.0 → 0.1
Time: 7.0s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}
double f(double x, double y) {
        double r322376 = x;
        double r322377 = y;
        double r322378 = 1.0;
        double r322379 = r322376 * r322377;
        double r322380 = 2.0;
        double r322381 = r322379 / r322380;
        double r322382 = r322378 + r322381;
        double r322383 = r322377 / r322382;
        double r322384 = r322376 - r322383;
        return r322384;
}
↓
double f(double x, double y) {
        double r322385 = x;
        double r322386 = y;
        double r322387 = 1.0;
        double r322388 = 1.0;
        double r322389 = r322385 * r322386;
        double r322390 = 2.0;
        double r322391 = r322389 / r322390;
        double r322392 = r322388 + r322391;
        double r322393 = r322387 / r322392;
        double r322394 = r322386 * r322393;
        double r322395 = r322385 - r322394;
        return r322395;
}

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 div-inv0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))