Average Error: 0.4 → 0.2
Time: 1.9s
Precision: binary64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{x + y} \cdot 100\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{x + y} \cdot 100
double code(double x, double y) {
	return ((double) (((double) (x * 100.0)) / ((double) (x + y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x / ((double) (x + y)))) * 100.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.4

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

  2. Simplified0.2

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

  4. Applied clear-num0.3

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

  6. Applied associate-/r/0.3

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

  7. Applied associate-*r*0.3

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020181 
(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)))