Average Error: 52.0 → 52.0
Time: 9.7s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r48719 = 9.0;
        double r48720 = x;
        double r48721 = 4.0;
        double r48722 = pow(r48720, r48721);
        double r48723 = r48719 * r48722;
        double r48724 = y;
        double r48725 = pow(r48724, r48721);
        double r48726 = r48723 - r48725;
        double r48727 = 2.0;
        double r48728 = r48724 * r48724;
        double r48729 = r48727 * r48728;
        double r48730 = r48726 + r48729;
        return r48730;
}
↓
double f(double x, double y) {
        double r48731 = 9.0;
        double r48732 = x;
        double r48733 = 4.0;
        double r48734 = pow(r48732, r48733);
        double r48735 = r48731 * r48734;
        double r48736 = y;
        double r48737 = pow(r48736, r48733);
        double r48738 = r48735 - r48737;
        double r48739 = 3.0;
        double r48740 = pow(r48738, r48739);
        double r48741 = cbrt(r48740);
        double r48742 = 2.0;
        double r48743 = r48736 * r48736;
        double r48744 = r48742 * r48743;
        double r48745 = r48741 + r48744;
        return r48745;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 52.0

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

  3. Applied add-cbrt-cube52.0

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

  4. Simplified52.0

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))