Average Error: 62.0 → 52.0
Time: 17.5s
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 r37881 = 9.0;
        double r37882 = x;
        double r37883 = 4.0;
        double r37884 = pow(r37882, r37883);
        double r37885 = r37881 * r37884;
        double r37886 = y;
        double r37887 = r37886 * r37886;
        double r37888 = 2.0;
        double r37889 = r37887 - r37888;
        double r37890 = r37887 * r37889;
        double r37891 = r37885 - r37890;
        return r37891;
}
↓
double f(double x, double y) {
        double r37892 = 9.0;
        double r37893 = x;
        double r37894 = 4.0;
        double r37895 = pow(r37893, r37894);
        double r37896 = r37892 * r37895;
        double r37897 = y;
        double r37898 = 4.0;
        double r37899 = pow(r37897, r37898);
        double r37900 = r37896 - r37899;
        double r37901 = 3.0;
        double r37902 = pow(r37900, r37901);
        double r37903 = cbrt(r37902);
        double r37904 = 2.0;
        double r37905 = -r37904;
        double r37906 = r37897 * r37897;
        double r37907 = r37905 * r37906;
        double r37908 = r37903 - r37907;
        return r37908;
}

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 2019303 
(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))))