Average Error: 0.0 → 0.1
Time: 8.6s
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 r312851 = x;
        double r312852 = y;
        double r312853 = 1.0;
        double r312854 = r312851 * r312852;
        double r312855 = 2.0;
        double r312856 = r312854 / r312855;
        double r312857 = r312853 + r312856;
        double r312858 = r312852 / r312857;
        double r312859 = r312851 - r312858;
        return r312859;
}
↓
double f(double x, double y) {
        double r312860 = x;
        double r312861 = y;
        double r312862 = 1.0;
        double r312863 = 1.0;
        double r312864 = r312860 * r312861;
        double r312865 = 2.0;
        double r312866 = r312864 / r312865;
        double r312867 = r312863 + r312866;
        double r312868 = r312862 / r312867;
        double r312869 = r312861 * r312868;
        double r312870 = r312860 - r312869;
        return r312870;
}

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 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)))))