Average Error: 0.4 → 0.2
Time: 1.3s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[x \cdot \frac{100}{x + y}\]
\frac{x \cdot 100}{x + y}
↓
x \cdot \frac{100}{x + y}
double code(double x, double y) {
	return ((x * 100.0) / (x + y));
}
↓
double code(double x, double y) {
	return (x * (100.0 / (x + y)));
}

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. Using strategy rm

  3. Applied associate-/l*0.2

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

  5. Applied div-inv0.3

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1) (/ 100 (+ x y)))

  (/ (* x 100) (+ x y)))