Average Error: 0.0 → 0.1
Time: 14.7s
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 r215841 = x;
        double r215842 = y;
        double r215843 = 1.0;
        double r215844 = r215841 * r215842;
        double r215845 = 2.0;
        double r215846 = r215844 / r215845;
        double r215847 = r215843 + r215846;
        double r215848 = r215842 / r215847;
        double r215849 = r215841 - r215848;
        return r215849;
}
↓
double f(double x, double y) {
        double r215850 = x;
        double r215851 = 1.0;
        double r215852 = 0.5;
        double r215853 = r215852 * r215850;
        double r215854 = 1.0;
        double r215855 = y;
        double r215856 = r215854 / r215855;
        double r215857 = r215853 + r215856;
        double r215858 = r215851 / r215857;
        double r215859 = r215850 - r215858;
        return r215859;
}

Error

Bits error versus x

Bits error versus y

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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 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))