Average Error: 0.4 → 0.2
Time: 1.3s
Precision: binary64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{\frac{x}{x + y}}{0.01}\]
\frac{x \cdot 100}{x + y}
↓
\frac{\frac{x}{x + y}}{0.01}
(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))
↓
(FPCore (x y) :precision binary64 (/ (/ x (+ x y)) 0.01))
double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
↓
double code(double x, double y) {
	return (x / (x + y)) / 0.01;
}

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*_binary640.2

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

  5. Applied div-inv_binary640.2

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

  6. Applied associate-/r*_binary640.2

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

  7. Final simplification0.2

    \[\leadsto \frac{\frac{x}{x + y}}{0.01}\]

Reproduce

herbie shell --seed 2020224 
(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)))