Average Error: 0.0 → 0.0
Time: 5.8s
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 r4824 = x;
        double r4825 = y;
        double r4826 = r4824 + r4825;
        double r4827 = 10.0;
        double r4828 = r4826 / r4827;
        return r4828;
}
↓
double f(double x, double y) {
        double r4829 = y;
        double r4830 = 10.0;
        double r4831 = r4829 / r4830;
        double r4832 = x;
        double r4833 = r4832 / r4830;
        double r4834 = r4831 + r4833;
        return r4834;
}

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))