Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.4 → 0.2

Time: 8.2s

Precision: 64

Math

\[\frac{x \cdot 100}{x + y}\]

↓

\[\frac{\sqrt{100}}{\frac{1}{\sqrt{100}}} \cdot \frac{x}{y + x}\]

C

double f(double x, double y) {
        double r528564 = x;
        double r528565 = 100.0;
        double r528566 = r528564 * r528565;
        double r528567 = y;
        double r528568 = r528564 + r528567;
        double r528569 = r528566 / r528568;
        return r528569;
}

↓

double f(double x, double y) {
        double r528570 = 100.0;
        double r528571 = sqrt(r528570);
        double r528572 = 1.0;
        double r528573 = r528572 / r528571;
        double r528574 = r528571 / r528573;
        double r528575 = x;
        double r528576 = y;
        double r528577 = r528576 + r528575;
        double r528578 = r528575 / r528577;
        double r528579 = r528574 * r528578;
        return r528579;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.4
Target	0.2
Herbie	0.2

\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

1. Initial program 0.4

   \[\frac{x \cdot 100}{x + y}\]

2. Simplified 0.4

   \[\leadsto \color{blue}{\frac{x \cdot 100}{y + x}}\]
3. Using strategy rm

4. Applied *-un-lft-identity 0.4

   \[\leadsto \frac{x \cdot 100}{\color{blue}{1 \cdot \left(y + x\right)}}\]

5. Applied times-frac 0.2

   \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{100}{y + x}}\]

6. Simplified 0.2

   \[\leadsto \color{blue}{x} \cdot \frac{100}{y + x}\]
7. Using strategy rm

8. Applied add-sqr-sqrt 0.2

   \[\leadsto x \cdot \frac{\color{blue}{\sqrt{100} \cdot \sqrt{100}}}{y + x}\]

9. Applied associate-/l* 0.3

   \[\leadsto x \cdot \color{blue}{\frac{\sqrt{100}}{\frac{y + x}{\sqrt{100}}}}\]
10. Using strategy rm

11. Applied div-inv 0.4

    \[\leadsto x \cdot \frac{\sqrt{100}}{\color{blue}{\left(y + x\right) \cdot \frac{1}{\sqrt{100}}}}\]

12. Applied *-un-lft-identity 0.4

    \[\leadsto x \cdot \frac{\sqrt{\color{blue}{1 \cdot 100}}}{\left(y + x\right) \cdot \frac{1}{\sqrt{100}}}\]

13. Applied sqrt-prod 0.4

    \[\leadsto x \cdot \frac{\color{blue}{\sqrt{1} \cdot \sqrt{100}}}{\left(y + x\right) \cdot \frac{1}{\sqrt{100}}}\]

14. Applied times-frac 0.3

    \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt{1}}{y + x} \cdot \frac{\sqrt{100}}{\frac{1}{\sqrt{100}}}\right)}\]

15. Applied associate-*r* 0.3

    \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt{1}}{y + x}\right) \cdot \frac{\sqrt{100}}{\frac{1}{\sqrt{100}}}}\]

16. Simplified 0.2

    \[\leadsto \color{blue}{\frac{x}{x + y}} \cdot \frac{\sqrt{100}}{\frac{1}{\sqrt{100}}}\]

17. Final simplification 0.2

    \[\leadsto \frac{\sqrt{100}}{\frac{1}{\sqrt{100}}} \cdot \frac{x}{y + x}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))