Average Error: 0.3 → 0.2
Time: 2.2s
Precision: binary64
\[\frac{x \cdot 100}{x + y} \]
↓
\[10 \cdot \frac{x}{\frac{x + y}{10}} \]
\frac{x \cdot 100}{x + y}
↓
10 \cdot \frac{x}{\frac{x + y}{10}}

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))
↓
(FPCore (x y) :precision binary64 (* 10.0 (/ x (/ (+ x y) 10.0))))
double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
↓
double code(double x, double y) {
	return 10.0 * (x / ((x + y) / 10.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y} \]

Derivation

  1. Initial program 0.3

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

  2. Applied associate-/l*_binary640.2

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

  3. Applied add-sqr-sqrt_binary640.2

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

  4. Applied *-un-lft-identity_binary640.2

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

  5. Applied times-frac_binary640.4

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

  6. Applied *-un-lft-identity_binary640.4

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

  7. Applied times-frac_binary640.2

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

  8. Simplified0.2

    \[\leadsto \color{blue}{10} \cdot \frac{x}{\frac{x + y}{\sqrt{100}}} \]

  9. Simplified0.2

    \[\leadsto 10 \cdot \color{blue}{\frac{x}{\frac{x + y}{10}}} \]

  10. Final simplification0.2

    \[\leadsto 10 \cdot \frac{x}{\frac{x + y}{10}} \]

Reproduce

herbie shell --seed 2022077 
(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)))