Average Error: 62.0 → 51.4
Time: 9.0s
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 r44255 = 9.0;
        double r44256 = x;
        double r44257 = 4.0;
        double r44258 = pow(r44256, r44257);
        double r44259 = r44255 * r44258;
        double r44260 = y;
        double r44261 = r44260 * r44260;
        double r44262 = 2.0;
        double r44263 = r44261 - r44262;
        double r44264 = r44261 * r44263;
        double r44265 = r44259 - r44264;
        return r44265;
}
↓
double f(double x, double y) {
        double r44266 = y;
        double r44267 = 2.0;
        double r44268 = r44266 * r44267;
        double r44269 = r44266 * r44268;
        double r44270 = 4.0;
        double r44271 = pow(r44266, r44270);
        double r44272 = 9.0;
        double r44273 = x;
        double r44274 = 4.0;
        double r44275 = pow(r44273, r44274);
        double r44276 = r44272 * r44275;
        double r44277 = r44271 - r44276;
        double r44278 = log(r44277);
        double r44279 = sqrt(r44278);
        double r44280 = cbrt(r44279);
        double r44281 = r44280 * r44280;
        double r44282 = exp(r44281);
        double r44283 = 8.0;
        double r44284 = pow(r44266, r44283);
        double r44285 = r44272 * r44272;
        double r44286 = 2.0;
        double r44287 = r44286 * r44274;
        double r44288 = pow(r44273, r44287);
        double r44289 = r44285 * r44288;
        double r44290 = r44284 - r44289;
        double r44291 = r44276 + r44271;
        double r44292 = r44290 / r44291;
        double r44293 = log(r44292);
        double r44294 = sqrt(r44293);
        double r44295 = cbrt(r44294);
        double r44296 = r44279 * r44295;
        double r44297 = pow(r44282, r44296);
        double r44298 = r44269 - r44297;
        return r44298;
}

Error

Try it out

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. 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))))