Average Error: 0.5 → 0.2
Time: 1.7s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x \cdot 1}{\frac{x + y}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{x \cdot 1}{\frac{x + y}{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 * 1.0)) / ((double) (((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

Original0.5
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.5

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

  3. Applied *-un-lft-identity0.5

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

  4. Applied associate-*r*0.5

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

  5. Applied associate-/l*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020114 
(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)))