Average Error: 62.0 → 51.4
Time: 9.1s
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 r44004 = 9.0;
        double r44005 = x;
        double r44006 = 4.0;
        double r44007 = pow(r44005, r44006);
        double r44008 = r44004 * r44007;
        double r44009 = y;
        double r44010 = r44009 * r44009;
        double r44011 = 2.0;
        double r44012 = r44010 - r44011;
        double r44013 = r44010 * r44012;
        double r44014 = r44008 - r44013;
        return r44014;
}
↓
double f(double x, double y) {
        double r44015 = y;
        double r44016 = 2.0;
        double r44017 = r44015 * r44016;
        double r44018 = r44015 * r44017;
        double r44019 = 4.0;
        double r44020 = pow(r44015, r44019);
        double r44021 = 9.0;
        double r44022 = x;
        double r44023 = 4.0;
        double r44024 = pow(r44022, r44023);
        double r44025 = r44021 * r44024;
        double r44026 = r44020 - r44025;
        double r44027 = log(r44026);
        double r44028 = sqrt(r44027);
        double r44029 = cbrt(r44028);
        double r44030 = r44029 * r44029;
        double r44031 = exp(r44030);
        double r44032 = 8.0;
        double r44033 = pow(r44015, r44032);
        double r44034 = r44021 * r44021;
        double r44035 = 2.0;
        double r44036 = r44035 * r44023;
        double r44037 = pow(r44022, r44036);
        double r44038 = r44034 * r44037;
        double r44039 = r44033 - r44038;
        double r44040 = r44025 + r44020;
        double r44041 = r44039 / r44040;
        double r44042 = log(r44041);
        double r44043 = sqrt(r44042);
        double r44044 = cbrt(r44043);
        double r44045 = r44028 * r44044;
        double r44046 = pow(r44031, r44045);
        double r44047 = r44018 - r44046;
        return r44047;
}

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 2019195 
(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))))