Average Error: 52.0 → 52.0
Time: 10.5s
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 r2758095 = 9.0;
        double r2758096 = x;
        double r2758097 = 4.0;
        double r2758098 = pow(r2758096, r2758097);
        double r2758099 = r2758095 * r2758098;
        double r2758100 = y;
        double r2758101 = pow(r2758100, r2758097);
        double r2758102 = r2758099 - r2758101;
        double r2758103 = 2.0;
        double r2758104 = r2758100 * r2758100;
        double r2758105 = r2758103 * r2758104;
        double r2758106 = r2758102 + r2758105;
        return r2758106;
}
↓
double f(double x, double y) {
        double r2758107 = 2.0;
        double r2758108 = y;
        double r2758109 = r2758108 * r2758108;
        double r2758110 = r2758107 * r2758109;
        double r2758111 = x;
        double r2758112 = 4.0;
        double r2758113 = pow(r2758111, r2758112);
        double r2758114 = 9.0;
        double r2758115 = r2758113 * r2758114;
        double r2758116 = pow(r2758108, r2758112);
        double r2758117 = r2758115 - r2758116;
        double r2758118 = r2758117 * r2758117;
        double r2758119 = r2758117 * r2758118;
        double r2758120 = cbrt(r2758119);
        double r2758121 = r2758110 + r2758120;
        return r2758121;
}

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 2019172 
(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))))