Average Error: 52.0 → 52.0
Time: 2.5s
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 r69424 = 9.0;
        double r69425 = x;
        double r69426 = 4.0;
        double r69427 = pow(r69425, r69426);
        double r69428 = r69424 * r69427;
        double r69429 = y;
        double r69430 = pow(r69429, r69426);
        double r69431 = r69428 - r69430;
        double r69432 = 2.0;
        double r69433 = r69429 * r69429;
        double r69434 = r69432 * r69433;
        double r69435 = r69431 + r69434;
        return r69435;
}
↓
double f(double x, double y) {
        double r69436 = 9.0;
        double r69437 = x;
        double r69438 = 4.0;
        double r69439 = pow(r69437, r69438);
        double r69440 = r69436 * r69439;
        double r69441 = y;
        double r69442 = pow(r69441, r69438);
        double r69443 = r69440 - r69442;
        double r69444 = 3.0;
        double r69445 = pow(r69443, r69444);
        double r69446 = cbrt(r69445);
        double r69447 = 2.0;
        double r69448 = r69441 * r69441;
        double r69449 = r69447 * r69448;
        double r69450 = r69446 + r69449;
        return r69450;
}

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 2019362 +o rules:numerics
(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))))