Average Error: 62.0 → 52.0
Time: 14.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{\left(\left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)} - \left(-2\right) \cdot \left(y \cdot y\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{\left(\left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)} - \left(-2\right) \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r3739900 = 9.0;
        double r3739901 = x;
        double r3739902 = 4.0;
        double r3739903 = pow(r3739901, r3739902);
        double r3739904 = r3739900 * r3739903;
        double r3739905 = y;
        double r3739906 = r3739905 * r3739905;
        double r3739907 = 2.0;
        double r3739908 = r3739906 - r3739907;
        double r3739909 = r3739906 * r3739908;
        double r3739910 = r3739904 - r3739909;
        return r3739910;
}
↓
double f(double x, double y) {
        double r3739911 = x;
        double r3739912 = 4.0;
        double r3739913 = pow(r3739911, r3739912);
        double r3739914 = 9.0;
        double r3739915 = r3739913 * r3739914;
        double r3739916 = y;
        double r3739917 = r3739916 * r3739916;
        double r3739918 = r3739917 * r3739917;
        double r3739919 = r3739915 - r3739918;
        double r3739920 = r3739919 * r3739919;
        double r3739921 = r3739920 * r3739919;
        double r3739922 = cbrt(r3739921);
        double r3739923 = 2.0;
        double r3739924 = -r3739923;
        double r3739925 = r3739924 * r3739917;
        double r3739926 = r3739922 - r3739925;
        return r3739926;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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-lft-in62.0

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

  5. Applied associate--r+52.0

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

  7. Applied add-cbrt-cube52.0

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

  8. Final simplification52.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))