Average Error: 62.0 → 0
Time: 3.0s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {y}^{2}\right) \cdot \left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {y}^{2}\right) - \left(-2\right) \cdot \left(y \cdot y\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {y}^{2}\right) \cdot \left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {y}^{2}\right) - \left(-2\right) \cdot \left(y \cdot y\right)
double code(double x, double y) {
	return ((double) (((double) (9.0 * ((double) pow(x, 4.0)))) - ((double) (((double) (y * y)) * ((double) (((double) (y * y)) - 2.0))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) (((double) sqrt(9.0)) * ((double) sqrt(((double) pow(x, 4.0)))))) + ((double) pow(y, 2.0)))) * ((double) (((double) (((double) sqrt(9.0)) * ((double) sqrt(((double) pow(x, 4.0)))))) - ((double) pow(y, 2.0)))))) - ((double) (((double) -(2.0)) * ((double) (y * y))))));
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg62.0

    \[\leadsto 9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot y + \left(-2\right)\right)}\]

  4. Applied distribute-rgt-in62.0

    \[\leadsto 9 \cdot {x}^{4} - \color{blue}{\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right) + \left(-2\right) \cdot \left(y \cdot y\right)\right)}\]

  5. Applied associate--r+52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) - \left(-2\right) \cdot \left(y \cdot y\right)}\]

  6. Simplified52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)} - \left(-2\right) \cdot \left(y \cdot y\right)\]
  7. Using strategy rm

  8. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  9. Simplified52.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}} - \left(-2\right) \cdot \left(y \cdot y\right)\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt52.0

    \[\leadsto \sqrt[3]{{\left(9 \cdot {x}^{4} - {\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  12. Applied unpow-prod-down54.5

    \[\leadsto \sqrt[3]{{\left(9 \cdot {x}^{4} - \color{blue}{{\left(\sqrt{y}\right)}^{4} \cdot {\left(\sqrt{y}\right)}^{4}}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  13. Applied add-sqr-sqrt54.5

    \[\leadsto \sqrt[3]{{\left(9 \cdot \color{blue}{\left(\sqrt{{x}^{4}} \cdot \sqrt{{x}^{4}}\right)} - {\left(\sqrt{y}\right)}^{4} \cdot {\left(\sqrt{y}\right)}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  14. Applied add-sqr-sqrt54.5

    \[\leadsto \sqrt[3]{{\left(\color{blue}{\left(\sqrt{9} \cdot \sqrt{9}\right)} \cdot \left(\sqrt{{x}^{4}} \cdot \sqrt{{x}^{4}}\right) - {\left(\sqrt{y}\right)}^{4} \cdot {\left(\sqrt{y}\right)}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  15. Applied unswap-sqr54.5

    \[\leadsto \sqrt[3]{{\left(\color{blue}{\left(\sqrt{9} \cdot \sqrt{{x}^{4}}\right) \cdot \left(\sqrt{9} \cdot \sqrt{{x}^{4}}\right)} - {\left(\sqrt{y}\right)}^{4} \cdot {\left(\sqrt{y}\right)}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  16. Applied difference-of-squares54.4

    \[\leadsto \sqrt[3]{{\color{blue}{\left(\left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {\left(\sqrt{y}\right)}^{4}\right) \cdot \left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {\left(\sqrt{y}\right)}^{4}\right)\right)}}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  17. Applied unpow-prod-down54.4

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {\left(\sqrt{y}\right)}^{4}\right)}^{3} \cdot {\left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {\left(\sqrt{y}\right)}^{4}\right)}^{3}}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  18. Applied cbrt-prod54.4

    \[\leadsto \color{blue}{\sqrt[3]{{\left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {\left(\sqrt{y}\right)}^{4}\right)}^{3}} \cdot \sqrt[3]{{\left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {\left(\sqrt{y}\right)}^{4}\right)}^{3}}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  19. Simplified54.4

    \[\leadsto \color{blue}{\left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {y}^{2}\right)} \cdot \sqrt[3]{{\left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {\left(\sqrt{y}\right)}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  20. Simplified0

    \[\leadsto \left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {y}^{2}\right) \cdot \color{blue}{\left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {y}^{2}\right)} - \left(-2\right) \cdot \left(y \cdot y\right)\]

  21. Final simplification0

    \[\leadsto \left(\sqrt{9} \cdot \sqrt{{x}^{4}} + {y}^{2}\right) \cdot \left(\sqrt{9} \cdot \sqrt{{x}^{4}} - {y}^{2}\right) - \left(-2\right) \cdot \left(y \cdot y\right)\]

Reproduce

herbie shell --seed 2020114 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (- (* 9 (pow x 4)) (* (* y y) (- (* y y) 2))))