Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.3 → 0.2

Time: 7.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r558414 = x;
        double r558415 = 100.0;
        double r558416 = r558414 * r558415;
        double r558417 = y;
        double r558418 = r558414 + r558417;
        double r558419 = r558416 / r558418;
        return r558419;
}

↓

double f(double x, double y) {
        double r558420 = x;
        double r558421 = y;
        double r558422 = r558420 + r558421;
        double r558423 = r558420 / r558422;
        double r558424 = 100.0;
        double r558425 = r558423 * r558424;
        return r558425;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

   \[\frac{x \cdot 100}{x + y}\]
2. Using strategy rm

3. Applied clear-num 0.7

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

4. Simplified 0.5

   \[\leadsto \frac{1}{\color{blue}{\frac{\frac{y + x}{x}}{100}}}\]
5. Using strategy rm

6. Applied div-inv 0.5

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

7. Applied add-sqr-sqrt 0.5

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

8. Applied times-frac 0.5

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

9. Simplified 0.2

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

10. Simplified 0.2

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

11. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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)))