Average Error: 62.0 → 51.4
Time: 9.2s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[y \cdot \left(y \cdot 2\right) - {\left(e^{\sqrt[3]{\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)}} \cdot \sqrt[3]{\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)}}}\right)}^{\left(\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)} \cdot \sqrt[3]{\sqrt{\log \left(\frac{{y}^{8} - \left(9 \cdot 9\right) \cdot {x}^{\left(2 \cdot 4\right)}}{9 \cdot {x}^{4} + {y}^{4}}\right)}}\right)}\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
y \cdot \left(y \cdot 2\right) - {\left(e^{\sqrt[3]{\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)}} \cdot \sqrt[3]{\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)}}}\right)}^{\left(\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)} \cdot \sqrt[3]{\sqrt{\log \left(\frac{{y}^{8} - \left(9 \cdot 9\right) \cdot {x}^{\left(2 \cdot 4\right)}}{9 \cdot {x}^{4} + {y}^{4}}\right)}}\right)}
double f(double x, double y) {
        double r31946 = 9.0;
        double r31947 = x;
        double r31948 = 4.0;
        double r31949 = pow(r31947, r31948);
        double r31950 = r31946 * r31949;
        double r31951 = y;
        double r31952 = r31951 * r31951;
        double r31953 = 2.0;
        double r31954 = r31952 - r31953;
        double r31955 = r31952 * r31954;
        double r31956 = r31950 - r31955;
        return r31956;
}
↓
double f(double x, double y) {
        double r31957 = y;
        double r31958 = 2.0;
        double r31959 = r31957 * r31958;
        double r31960 = r31957 * r31959;
        double r31961 = 4.0;
        double r31962 = pow(r31957, r31961);
        double r31963 = 9.0;
        double r31964 = x;
        double r31965 = 4.0;
        double r31966 = pow(r31964, r31965);
        double r31967 = r31963 * r31966;
        double r31968 = r31962 - r31967;
        double r31969 = log(r31968);
        double r31970 = sqrt(r31969);
        double r31971 = cbrt(r31970);
        double r31972 = r31971 * r31971;
        double r31973 = exp(r31972);
        double r31974 = 8.0;
        double r31975 = pow(r31957, r31974);
        double r31976 = r31963 * r31963;
        double r31977 = 2.0;
        double r31978 = r31977 * r31965;
        double r31979 = pow(r31964, r31978);
        double r31980 = r31976 * r31979;
        double r31981 = r31975 - r31980;
        double r31982 = r31967 + r31962;
        double r31983 = r31981 / r31982;
        double r31984 = log(r31983);
        double r31985 = sqrt(r31984);
        double r31986 = cbrt(r31985);
        double r31987 = r31970 * r31986;
        double r31988 = pow(r31973, r31987);
        double r31989 = r31960 - r31988;
        return r31989;
}

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. Simplified52.0

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

  4. Applied add-exp-log52.0

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

  5. Simplified52.0

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

  7. Applied add-sqr-sqrt52.0

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

  8. Applied exp-prod52.0

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

  9. Simplified52.0

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

  11. Applied add-cube-cbrt52.0

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

  12. Applied exp-prod52.0

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

  13. Applied pow-pow52.0

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

  14. Simplified52.0

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

  16. Applied flip--52.1

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

  17. Simplified51.4

    \[\leadsto y \cdot \left(y \cdot 2\right) - {\left(e^{\sqrt[3]{\sqrt{\log \left({y}^{4} - {x}^{4} \cdot 9\right)}} \cdot \sqrt[3]{\sqrt{\log \left({y}^{4} - {x}^{4} \cdot 9\right)}}}\right)}^{\left(\sqrt{\log \left({y}^{4} - {x}^{4} \cdot 9\right)} \cdot \sqrt[3]{\sqrt{\log \left(\frac{\color{blue}{{y}^{8} - \left(9 \cdot 9\right) \cdot {x}^{\left(4 \cdot 2\right)}}}{{y}^{4} + {x}^{4} \cdot 9}\right)}}\right)}\]

  18. Simplified51.4

    \[\leadsto y \cdot \left(y \cdot 2\right) - {\left(e^{\sqrt[3]{\sqrt{\log \left({y}^{4} - {x}^{4} \cdot 9\right)}} \cdot \sqrt[3]{\sqrt{\log \left({y}^{4} - {x}^{4} \cdot 9\right)}}}\right)}^{\left(\sqrt{\log \left({y}^{4} - {x}^{4} \cdot 9\right)} \cdot \sqrt[3]{\sqrt{\log \left(\frac{{y}^{8} - \left(9 \cdot 9\right) \cdot {x}^{\left(4 \cdot 2\right)}}{\color{blue}{9 \cdot {x}^{4} + {y}^{4}}}\right)}}\right)}\]

  19. Final simplification51.4

    \[\leadsto y \cdot \left(y \cdot 2\right) - {\left(e^{\sqrt[3]{\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)}} \cdot \sqrt[3]{\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)}}}\right)}^{\left(\sqrt{\log \left({y}^{4} - 9 \cdot {x}^{4}\right)} \cdot \sqrt[3]{\sqrt{\log \left(\frac{{y}^{8} - \left(9 \cdot 9\right) \cdot {x}^{\left(2 \cdot 4\right)}}{9 \cdot {x}^{4} + {y}^{4}}\right)}}\right)}\]

Reproduce

herbie shell --seed 2019194 
(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))))