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

Average Error: 0.0 → 0.0

Time: 10.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r16896 = x;
        double r16897 = y;
        double r16898 = r16896 + r16897;
        double r16899 = 10.0;
        double r16900 = r16898 / r16899;
        return r16900;
}

↓

double f(double x, double y) {
        double r16901 = x;
        double r16902 = 10.0;
        double r16903 = r16901 / r16902;
        double r16904 = y;
        double r16905 = r16904 / r16902;
        double r16906 = r16903 + r16905;
        return r16906;
}

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. Simplified 0.3

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

6. Applied *-un-lft-identity 0.3

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

7. Applied add-sqr-sqrt 1.0

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

8. Applied times-frac 0.7

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

9. Applied associate-/r* 0.3

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

10. Simplified 0.3

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

11. Taylor expanded around 0 1.1

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

12. Simplified 0.0

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

13. Final simplification 0.0

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

Reproduce

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