Average Error: 0.0 → 0.0
Time: 6.0s
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 r5528 = x;
        double r5529 = y;
        double r5530 = r5528 + r5529;
        double r5531 = 10.0;
        double r5532 = r5530 / r5531;
        return r5532;
}
↓
double f(double x, double y) {
        double r5533 = y;
        double r5534 = 10.0;
        double r5535 = r5533 / r5534;
        double r5536 = x;
        double r5537 = r5536 / r5534;
        double r5538 = r5535 + r5537;
        return r5538;
}

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 add-sqr-sqrt1.1

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

  4. Applied *-un-lft-identity1.1

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

  5. Applied times-frac0.3

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

  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 2020045 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10))