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 r68352 = 9.0;
        double r68353 = x;
        double r68354 = 4.0;
        double r68355 = pow(r68353, r68354);
        double r68356 = r68352 * r68355;
        double r68357 = y;
        double r68358 = pow(r68357, r68354);
        double r68359 = r68356 - r68358;
        double r68360 = 2.0;
        double r68361 = r68357 * r68357;
        double r68362 = r68360 * r68361;
        double r68363 = r68359 + r68362;
        return r68363;
}
↓
double f(double x, double y) {
        double r68364 = 9.0;
        double r68365 = x;
        double r68366 = 4.0;
        double r68367 = pow(r68365, r68366);
        double r68368 = r68364 * r68367;
        double r68369 = y;
        double r68370 = pow(r68369, r68366);
        double r68371 = r68368 - r68370;
        double r68372 = 3.0;
        double r68373 = pow(r68371, r68372);
        double r68374 = cbrt(r68373);
        double r68375 = 2.0;
        double r68376 = r68369 * r68369;
        double r68377 = r68375 * r68376;
        double r68378 = r68374 + r68377;
        return r68378;
}

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 2020056 +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))))