Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
\[\frac{x + y}{10}\]
↓
\[\frac{y}{10} + \frac{x}{10}\]
\frac{x + y}{10}
↓
\frac{y}{10} + \frac{x}{10}
double f(double x, double y) {
        double r18553 = x;
        double r18554 = y;
        double r18555 = r18553 + r18554;
        double r18556 = 10.0;
        double r18557 = r18555 / r18556;
        return r18557;
}
↓
double f(double x, double y) {
        double r18558 = y;
        double r18559 = 10.0;
        double r18560 = r18558 / r18559;
        double r18561 = x;
        double r18562 = r18561 / r18559;
        double r18563 = r18560 + r18562;
        return r18563;
}

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

    \[\frac{x + y}{10}\]
  2. Using strategy rm

  3. Applied clear-num0.3

    \[\leadsto \color{blue}{\frac{1}{\frac{10}{x + y}}}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt31.7

    \[\leadsto \frac{1}{\color{blue}{\sqrt{\frac{10}{x + y}} \cdot \sqrt{\frac{10}{x + y}}}}\]

  6. Taylor expanded around 0 1.1

    \[\leadsto \color{blue}{\frac{x}{{\left(\sqrt{10}\right)}^{2}} + \frac{y}{{\left(\sqrt{10}\right)}^{2}}}\]

  7. Simplified0.0

    \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}}\]

  8. Final simplification0.0

    \[\leadsto \frac{y}{10} + \frac{x}{10}\]

Reproduce

herbie shell --seed 2019209 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10))