Average Error: 0.0 → 0.0
Time: 11.1s
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 r176498 = x;
        double r176499 = y;
        double r176500 = 1.0;
        double r176501 = r176498 * r176499;
        double r176502 = 2.0;
        double r176503 = r176501 / r176502;
        double r176504 = r176500 + r176503;
        double r176505 = r176499 / r176504;
        double r176506 = r176498 - r176505;
        return r176506;
}
↓
double f(double x, double y) {
        double r176507 = x;
        double r176508 = 1.0;
        double r176509 = 0.5;
        double r176510 = r176509 * r176507;
        double r176511 = 1.0;
        double r176512 = y;
        double r176513 = r176511 / r176512;
        double r176514 = r176510 + r176513;
        double r176515 = r176508 / r176514;
        double r176516 = r176507 - r176515;
        return r176516;
}

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 0.0

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

  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)))))