Average Error: 62.0 → 52.0
Time: 13.2s
Precision: binary64
Cost: 2112
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(\sqrt[3]{9 \cdot {x}^{4} - {y}^{4}} \cdot \sqrt[3]{{\left(\sqrt[3]{9 \cdot {x}^{4} - {y}^{4}}\right)}^{6}}\right)}^{3}} - \left(y \cdot y\right) \cdot -2\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{{\left(\sqrt[3]{9 \cdot {x}^{4} - {y}^{4}} \cdot \sqrt[3]{{\left(\sqrt[3]{9 \cdot {x}^{4} - {y}^{4}}\right)}^{6}}\right)}^{3}} - \left(y \cdot y\right) \cdot -2
(FPCore (x y)
 :precision binary64
 (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))
↓
(FPCore (x y)
 :precision binary64
 (-
  (cbrt
   (pow
    (*
     (cbrt (- (* 9.0 (pow x 4.0)) (pow y 4.0)))
     (cbrt (pow (cbrt (- (* 9.0 (pow x 4.0)) (pow y 4.0))) 6.0)))
    3.0))
  (* (* y y) -2.0)))
double code(double x, double y) {
	return (9.0 * pow(x, 4.0)) - ((y * y) * ((y * y) - 2.0));
}
↓
double code(double x, double y) {
	return cbrt(pow((cbrt((9.0 * pow(x, 4.0)) - pow(y, 4.0)) * cbrt(pow(cbrt((9.0 * pow(x, 4.0)) - pow(y, 4.0)), 6.0))), 3.0)) - ((y * y) * -2.0);
}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs
Alternative 1
Accuracy52.0
Cost960
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) - \left(y \cdot y\right) \cdot -2\]
Alternative 2
Accuracy52.0
Cost1216
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + \left(y \cdot y\right) \cdot \left(\sqrt{2} \cdot \sqrt{2}\right)\]
Alternative 3
Accuracy64.0
Cost1920
\[\sqrt[3]{{\left(\sqrt{9 \cdot {x}^{4} - {y}^{4}} \cdot \sqrt{9 \cdot {x}^{4} - {y}^{4}}\right)}^{3}} - \left(y \cdot y\right) \cdot -2\]

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-neg_binary64_109462.0

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

  4. Applied distribute-lft-in_binary64_105062.0

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

  5. Applied associate--r+_binary64_103752.0

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

  6. Simplified52.0

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

  8. Applied add-cbrt-cube_binary64_113752.0

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

  9. Simplified52.0

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

  11. Applied add-cube-cbrt_binary64_113652.0

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

  12. Simplified52.0

    \[\leadsto \sqrt[3]{{\left(\color{blue}{\sqrt[3]{{\left(\sqrt[3]{9 \cdot {x}^{4} - {y}^{4}}\right)}^{6}}} \cdot \sqrt[3]{9 \cdot {x}^{4} - {y}^{4}}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

  13. Final simplification52.0

    \[\leadsto \sqrt[3]{{\left(\sqrt[3]{9 \cdot {x}^{4} - {y}^{4}} \cdot \sqrt[3]{{\left(\sqrt[3]{9 \cdot {x}^{4} - {y}^{4}}\right)}^{6}}\right)}^{3}} - \left(y \cdot y\right) \cdot -2\]

Reproduce

herbie shell --seed 2020322 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))