Average Error: 0.0 → 0.0
Time: 18.8s
Precision: binary64
Cost: 448
\[\frac{x}{y + x}\]
↓
\[\frac{-x}{\left(-x\right) - y}\]
\frac{x}{y + x}
↓
\frac{-x}{\left(-x\right) - y}
(FPCore (x y) :precision binary64 (/ x (+ y x)))
↓
(FPCore (x y) :precision binary64 (/ (- x) (- (- x) y)))
double code(double x, double y) {
	return x / (y + x);
}
↓
double code(double x, double y) {
	return -x / (-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
Alternative 1
Accuracy1.2
Cost768
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{x + y}{\sqrt[3]{x}}}\]
Alternative 2
Accuracy1.2
Cost1024
\[\frac{\frac{x}{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}}}{\sqrt[3]{x + y}}\]
Alternative 3
Accuracy29.0
Cost897
\[\begin{array}{l} \mathbf{if}\;y \leq -5.607860854113499 \cdot 10^{+141}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\sqrt{y + x}}}{\sqrt{y + x}}\\ \end{array}\]
Alternative 4
Accuracy54.0
Cost64
\[0\]

Derivation

  1. Initial program 0.0

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

  3. Applied *-un-lft-identity_binary64_92850.0

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

  4. Applied *-un-lft-identity_binary64_92850.0

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

  5. Applied times-frac_binary64_92910.0

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

  6. Simplified0.0

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

  7. Simplified0.0

    \[\leadsto 1 \cdot \color{blue}{\frac{x}{x + y}}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity_binary64_92850.0

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

  10. Applied *-un-lft-identity_binary64_92850.0

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

  11. Applied times-frac_binary64_92910.0

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

  12. Simplified0.0

    \[\leadsto 1 \cdot \left(\color{blue}{1} \cdot \frac{x}{x + y}\right)\]
  13. Using strategy rm

  14. Applied frac-2neg_binary64_92960.0

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

  15. Simplified0.0

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

  16. Final simplification0.0

    \[\leadsto \frac{-x}{\left(-x\right) - y}\]

Reproduce

herbie shell --seed 2020322 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))