Average Error: 62.0 → 52.0
Time: 16.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r38892 = 9.0;
        double r38893 = x;
        double r38894 = 4.0;
        double r38895 = pow(r38893, r38894);
        double r38896 = r38892 * r38895;
        double r38897 = y;
        double r38898 = r38897 * r38897;
        double r38899 = 2.0;
        double r38900 = r38898 - r38899;
        double r38901 = r38898 * r38900;
        double r38902 = r38896 - r38901;
        return r38902;
}
↓
double f(double x, double y) {
        double r38903 = 9.0;
        double r38904 = x;
        double r38905 = 4.0;
        double r38906 = pow(r38904, r38905);
        double r38907 = r38903 * r38906;
        double r38908 = y;
        double r38909 = 4.0;
        double r38910 = pow(r38908, r38909);
        double r38911 = r38907 - r38910;
        double r38912 = 3.0;
        double r38913 = pow(r38911, r38912);
        double r38914 = cbrt(r38913);
        double r38915 = 2.0;
        double r38916 = -r38915;
        double r38917 = r38908 * r38908;
        double r38918 = r38916 * r38917;
        double r38919 = r38914 - r38918;
        return r38919;
}

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

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

  8. Applied add-cbrt-cube52.0

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

  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. Final simplification52.0

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

Reproduce

herbie shell --seed 2019347 
(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))))