Average Error: 0.0 → 0.0
Time: 8.9s
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 r13569 = x;
        double r13570 = y;
        double r13571 = r13569 + r13570;
        double r13572 = 10.0;
        double r13573 = r13571 / r13572;
        return r13573;
}
↓
double f(double x, double y) {
        double r13574 = y;
        double r13575 = 10.0;
        double r13576 = r13574 / r13575;
        double r13577 = x;
        double r13578 = r13577 / r13575;
        double r13579 = r13576 + r13578;
        return r13579;
}

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. Simplified0.0

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

  4. Applied add-sqr-sqrt1.1

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

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

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Taylor expanded around 0 1.1

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  (/ (+ x y) 10.0))