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 r37538 = 9.0;
        double r37539 = x;
        double r37540 = 4.0;
        double r37541 = pow(r37539, r37540);
        double r37542 = r37538 * r37541;
        double r37543 = y;
        double r37544 = pow(r37543, r37540);
        double r37545 = r37542 - r37544;
        double r37546 = 2.0;
        double r37547 = r37543 * r37543;
        double r37548 = r37546 * r37547;
        double r37549 = r37545 + r37548;
        return r37549;
}
↓
double f(double x, double y) {
        double r37550 = 9.0;
        double r37551 = x;
        double r37552 = 4.0;
        double r37553 = pow(r37551, r37552);
        double r37554 = r37550 * r37553;
        double r37555 = y;
        double r37556 = pow(r37555, r37552);
        double r37557 = r37554 - r37556;
        double r37558 = 3.0;
        double r37559 = pow(r37557, r37558);
        double r37560 = cbrt(r37559);
        double r37561 = 2.0;
        double r37562 = r37555 * r37555;
        double r37563 = r37561 * r37562;
        double r37564 = r37560 + r37563;
        return r37564;
}

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 2019235 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))