Average Error: 0.5 → 0.2
Time: 3.3s
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

Original0.5
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 associate-/l*_binary64_187780.2

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

  5. Applied add-sqr-sqrt_binary64_188550.2

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

  6. Applied *-un-lft-identity_binary64_188330.2

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

  7. Applied times-frac_binary64_188390.4

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

  8. Applied *-un-lft-identity_binary64_188330.4

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

  9. Applied times-frac_binary64_188390.2

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

  10. Simplified0.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2021043 
(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)))