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

Average Error: 0.0 → 0.0

Time: 1.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r3125 = x;
        double r3126 = y;
        double r3127 = r3125 + r3126;
        double r3128 = 10.0;
        double r3129 = r3127 / r3128;
        return r3129;
}

↓

double f(double x, double y) {
        double r3130 = x;
        double r3131 = 10.0;
        double r3132 = r3130 / r3131;
        double r3133 = y;
        double r3134 = r3133 / r3131;
        double r3135 = r3132 + r3134;
        return r3135;
}

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 div-inv 0.4

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

6. Applied add-cube-cbrt 0.4

   \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{10 \cdot \frac{1}{x + y}}\]

7. Applied times-frac 0.4

   \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{10} \cdot \frac{\sqrt[3]{1}}{\frac{1}{x + y}}}\]

8. Simplified 0.4

   \[\leadsto \color{blue}{\frac{1}{10}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{x + y}}\]

9. Simplified 0.4

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

11. Applied distribute-lft-in 0.4

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

12. Simplified 0.2

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

13. Simplified 0.0

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

14. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10))