Average Error: 0.0 → 0.0
Time: 11.8s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{1}{0.5 \cdot x + \frac{1}{y}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{1}{0.5 \cdot x + \frac{1}{y}}
double f(double x, double y) {
        double r132003 = x;
        double r132004 = y;
        double r132005 = 1.0;
        double r132006 = r132003 * r132004;
        double r132007 = 2.0;
        double r132008 = r132006 / r132007;
        double r132009 = r132005 + r132008;
        double r132010 = r132004 / r132009;
        double r132011 = r132003 - r132010;
        return r132011;
}
↓
double f(double x, double y) {
        double r132012 = x;
        double r132013 = 1.0;
        double r132014 = 0.5;
        double r132015 = r132014 * r132012;
        double r132016 = 1.0;
        double r132017 = y;
        double r132018 = r132016 / r132017;
        double r132019 = r132015 + r132018;
        double r132020 = r132013 / r132019;
        double r132021 = r132012 - r132020;
        return r132021;
}

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. Taylor expanded around 0 0.0

    \[\leadsto x - \frac{1}{\color{blue}{0.5 \cdot x + 1 \cdot \frac{1}{y}}}\]

  5. Simplified0.0

    \[\leadsto x - \frac{1}{\color{blue}{0.5 \cdot x + \frac{1}{y}}}\]

  6. Final simplification0.0

    \[\leadsto x - \frac{1}{0.5 \cdot x + \frac{1}{y}}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))