Average Error: 52.0 → 52.0
Time: 2.9s
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 r74452 = 9.0;
        double r74453 = x;
        double r74454 = 4.0;
        double r74455 = pow(r74453, r74454);
        double r74456 = r74452 * r74455;
        double r74457 = y;
        double r74458 = pow(r74457, r74454);
        double r74459 = r74456 - r74458;
        double r74460 = 2.0;
        double r74461 = r74457 * r74457;
        double r74462 = r74460 * r74461;
        double r74463 = r74459 + r74462;
        return r74463;
}
↓
double f(double x, double y) {
        double r74464 = 9.0;
        double r74465 = x;
        double r74466 = 4.0;
        double r74467 = pow(r74465, r74466);
        double r74468 = r74464 * r74467;
        double r74469 = y;
        double r74470 = pow(r74469, r74466);
        double r74471 = r74468 - r74470;
        double r74472 = 3.0;
        double r74473 = pow(r74471, r74472);
        double r74474 = cbrt(r74473);
        double r74475 = 2.0;
        double r74476 = r74469 * r74469;
        double r74477 = r74475 * r74476;
        double r74478 = r74474 + r74477;
        return r74478;
}

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 2020035 +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))))