Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.5 → 0.2

Time: 2.5s

Precision: 64

Math

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

↓

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

C

double code(double x, double y) {
	return ((double) (((double) (x * 100.0)) / ((double) (x + y))));
}

↓

double code(double x, double y) {
	return ((double) (((double) sqrt(100.0)) * ((double) (x / ((double) (((double) (x + y)) / ((double) sqrt(100.0))))))));
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.5
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.5

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

3. Applied associate-/l* 0.2

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

5. Applied add-sqr-sqrt 0.2

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

6. Applied *-un-lft-identity 0.2

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

7. Applied times-frac 0.4

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

8. Applied *-un-lft-identity 0.4

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

9. Applied times-frac 0.2

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

10. Simplified 0.2

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

11. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020129 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

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

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