Average Error: 0.2 → 0.3
Time: 10.2s
Precision: binary64
Cost: 384
\[\frac{x}{y \cdot 3}\]
↓
\[-\frac{\frac{x}{y}}{-3}\]
\frac{x}{y \cdot 3}
↓
-\frac{\frac{x}{y}}{-3}
(FPCore (x y) :precision binary64 (/ x (* y 3.0)))
↓
(FPCore (x y) :precision binary64 (- (/ (/ x y) -3.0)))
double code(double x, double y) {
	return x / (y * 3.0);
}
↓
double code(double x, double y) {
	return -((x / y) / -3.0);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.3
Herbie0.3
\[\frac{\frac{x}{y}}{3}\]

Alternatives

Alternative 1
Accuracy0.4
Cost384
\[\frac{-x}{y} \cdot -0.3333333333333333\]
Alternative 2
Accuracy0.7
Cost448
\[\frac{-1}{\frac{-3}{\frac{x}{y}}}\]
Alternative 3
Accuracy1.2
Cost896
\[\frac{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{3 \cdot \frac{\sqrt[3]{y}}{x}}\]
Alternative 4
Accuracy17.1
Cost1281
\[\begin{array}{l} \mathbf{if}\;x \leq -3.781520788195614 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{-\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt{y}}}{\frac{-3}{\frac{\sqrt[3]{x}}{\sqrt{y}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt{x}}{\sqrt[3]{y}} \cdot 0.3333333333333333\right)\\ \end{array}\]
Alternative 5
Accuracy33.0
Cost1088
\[\frac{\frac{-\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt{y}}}{\frac{-3}{\frac{\sqrt[3]{x}}{\sqrt{y}}}}\]

Derivation

  1. Initial program 0.2

    \[\frac{x}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied frac-2neg_binary64_243000.2

    \[\leadsto \color{blue}{\frac{-x}{-y \cdot 3}}\]

  4. Simplified0.2

    \[\leadsto \frac{-x}{\color{blue}{y \cdot -3}}\]
  5. Using strategy rm

  6. Applied associate-/r*_binary64_242330.3

    \[\leadsto \color{blue}{\frac{\frac{-x}{y}}{-3}}\]
  7. Using strategy rm

  8. Applied pow1_binary64_243500.3

    \[\leadsto \color{blue}{{\left(\frac{\frac{-x}{y}}{-3}\right)}^{1}}\]
  9. Using strategy rm

  10. Applied distribute-frac-neg_binary64_242520.3

    \[\leadsto {\left(\frac{\color{blue}{-\frac{x}{y}}}{-3}\right)}^{1}\]

  11. Applied distribute-frac-neg_binary64_242520.3

    \[\leadsto {\color{blue}{\left(-\frac{\frac{x}{y}}{-3}\right)}}^{1}\]

  12. Final simplification0.3

    \[\leadsto -\frac{\frac{x}{y}}{-3}\]

Reproduce

herbie shell --seed 2020338 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))