Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A

Average Error: 0.0 → 0.0

Time: 15.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r1419992 = x;
        double r1419993 = y;
        double r1419994 = r1419992 + r1419993;
        double r1419995 = 10.0;
        double r1419996 = r1419994 / r1419995;
        return r1419996;
}

↓

double f(double x, double y) {
        double r1419997 = y;
        double r1419998 = 10.0;
        double r1419999 = r1419997 / r1419998;
        double r1420000 = x;
        double r1420001 = r1420000 / r1419998;
        double r1420002 = r1419999 + r1420001;
        return r1420002;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.0

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

3. Applied clear-num 0.3

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

5. Applied *-un-lft-identity 0.3

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

6. Applied add-sqr-sqrt 1.0

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

7. Applied times-frac 0.7

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

8. Applied associate-/r* 0.3

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

9. Simplified 0.3

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

10. Taylor expanded around 0 1.1

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

11. Simplified 0.0

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

12. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  (/ (+ x y) 10.0))