Average Error: 62.0 → 51.4
Time: 9.4s
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 r31235 = 9.0;
        double r31236 = x;
        double r31237 = 4.0;
        double r31238 = pow(r31236, r31237);
        double r31239 = r31235 * r31238;
        double r31240 = y;
        double r31241 = r31240 * r31240;
        double r31242 = 2.0;
        double r31243 = r31241 - r31242;
        double r31244 = r31241 * r31243;
        double r31245 = r31239 - r31244;
        return r31245;
}
↓
double f(double x, double y) {
        double r31246 = y;
        double r31247 = 2.0;
        double r31248 = r31246 * r31247;
        double r31249 = r31246 * r31248;
        double r31250 = 4.0;
        double r31251 = pow(r31246, r31250);
        double r31252 = 9.0;
        double r31253 = x;
        double r31254 = 4.0;
        double r31255 = pow(r31253, r31254);
        double r31256 = r31252 * r31255;
        double r31257 = r31251 - r31256;
        double r31258 = log(r31257);
        double r31259 = sqrt(r31258);
        double r31260 = cbrt(r31259);
        double r31261 = r31260 * r31260;
        double r31262 = exp(r31261);
        double r31263 = 8.0;
        double r31264 = pow(r31246, r31263);
        double r31265 = r31252 * r31252;
        double r31266 = 2.0;
        double r31267 = r31266 * r31254;
        double r31268 = pow(r31253, r31267);
        double r31269 = r31265 * r31268;
        double r31270 = r31264 - r31269;
        double r31271 = r31256 + r31251;
        double r31272 = r31270 / r31271;
        double r31273 = log(r31272);
        double r31274 = sqrt(r31273);
        double r31275 = cbrt(r31274);
        double r31276 = r31259 * r31275;
        double r31277 = pow(r31262, r31276);
        double r31278 = r31249 - r31277;
        return r31278;
}

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 2019196 
(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))))