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

Average Error: 0.0 → 0.0

Time: 6.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y) {
        double r4983 = x;
        double r4984 = y;
        double r4985 = r4983 + r4984;
        double r4986 = 10.0;
        double r4987 = r4985 / r4986;
        return r4987;
}

↓

double f(double x, double y) {
        double r4988 = x;
        double r4989 = 10.0;
        double r4990 = r4988 / r4989;
        double r4991 = y;
        double r4992 = r4991 / r4989;
        double r4993 = r4990 + r4992;
        return r4993;
}

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 add-sqr-sqrt 1.1

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

4. Applied *-un-lft-identity 1.1

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

5. Applied times-frac 0.3

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

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. Simplified 0.0

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

8. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10))