Average Error: 52.0 → 52.0
Time: 7.1s
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 r37132 = 9.0;
        double r37133 = x;
        double r37134 = 4.0;
        double r37135 = pow(r37133, r37134);
        double r37136 = r37132 * r37135;
        double r37137 = y;
        double r37138 = pow(r37137, r37134);
        double r37139 = r37136 - r37138;
        double r37140 = 2.0;
        double r37141 = r37137 * r37137;
        double r37142 = r37140 * r37141;
        double r37143 = r37139 + r37142;
        return r37143;
}
↓
double f(double x, double y) {
        double r37144 = 9.0;
        double r37145 = x;
        double r37146 = 4.0;
        double r37147 = pow(r37145, r37146);
        double r37148 = r37144 * r37147;
        double r37149 = y;
        double r37150 = pow(r37149, r37146);
        double r37151 = r37148 - r37150;
        double r37152 = 3.0;
        double r37153 = pow(r37151, r37152);
        double r37154 = cbrt(r37153);
        double r37155 = 2.0;
        double r37156 = r37149 * r37149;
        double r37157 = r37155 * r37156;
        double r37158 = r37154 + r37157;
        return r37158;
}

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 2019195 
(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))))