Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - y \cdot \frac{1}{1 + \frac{1}{\frac{\frac{2}{x}}{y}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - y \cdot \frac{1}{1 + \frac{1}{\frac{\frac{2}{x}}{y}}}
double f(double x, double y) {
        double r313469 = x;
        double r313470 = y;
        double r313471 = 1.0;
        double r313472 = r313469 * r313470;
        double r313473 = 2.0;
        double r313474 = r313472 / r313473;
        double r313475 = r313471 + r313474;
        double r313476 = r313470 / r313475;
        double r313477 = r313469 - r313476;
        return r313477;
}
↓
double f(double x, double y) {
        double r313478 = x;
        double r313479 = y;
        double r313480 = 1.0;
        double r313481 = 1.0;
        double r313482 = 2.0;
        double r313483 = r313482 / r313478;
        double r313484 = r313483 / r313479;
        double r313485 = r313480 / r313484;
        double r313486 = r313481 + r313485;
        double r313487 = r313480 / r313486;
        double r313488 = r313479 * r313487;
        double r313489 = r313478 - r313488;
        return r313489;
}

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. Using strategy rm

  5. Applied clear-num0.1

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))