Average Error: 52.0 → 52.0
Time: 13.6s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r3989120 = 9.0;
        double r3989121 = x;
        double r3989122 = 4.0;
        double r3989123 = pow(r3989121, r3989122);
        double r3989124 = r3989120 * r3989123;
        double r3989125 = y;
        double r3989126 = pow(r3989125, r3989122);
        double r3989127 = r3989124 - r3989126;
        double r3989128 = 2.0;
        double r3989129 = r3989125 * r3989125;
        double r3989130 = r3989128 * r3989129;
        double r3989131 = r3989127 + r3989130;
        return r3989131;
}
↓
double f(double x, double y) {
        double r3989132 = 2.0;
        double r3989133 = y;
        double r3989134 = r3989133 * r3989133;
        double r3989135 = r3989132 * r3989134;
        double r3989136 = x;
        double r3989137 = 4.0;
        double r3989138 = pow(r3989136, r3989137);
        double r3989139 = 9.0;
        double r3989140 = r3989138 * r3989139;
        double r3989141 = pow(r3989133, r3989137);
        double r3989142 = r3989140 - r3989141;
        double r3989143 = r3989142 * r3989142;
        double r3989144 = r3989142 * r3989143;
        double r3989145 = cbrt(r3989144);
        double r3989146 = r3989135 + r3989145;
        return r3989146;
}

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. Final simplification52.0

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

Reproduce

herbie shell --seed 2019169 
(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))))