Average Error: 52.0 → 52.0
Time: 12.2s
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 r46483 = 9.0;
        double r46484 = x;
        double r46485 = 4.0;
        double r46486 = pow(r46484, r46485);
        double r46487 = r46483 * r46486;
        double r46488 = y;
        double r46489 = pow(r46488, r46485);
        double r46490 = r46487 - r46489;
        double r46491 = 2.0;
        double r46492 = r46488 * r46488;
        double r46493 = r46491 * r46492;
        double r46494 = r46490 + r46493;
        return r46494;
}
↓
double f(double x, double y) {
        double r46495 = 9.0;
        double r46496 = x;
        double r46497 = 4.0;
        double r46498 = pow(r46496, r46497);
        double r46499 = r46495 * r46498;
        double r46500 = y;
        double r46501 = pow(r46500, r46497);
        double r46502 = r46499 - r46501;
        double r46503 = 3.0;
        double r46504 = pow(r46502, r46503);
        double r46505 = cbrt(r46504);
        double r46506 = 2.0;
        double r46507 = r46500 * r46500;
        double r46508 = r46506 * r46507;
        double r46509 = r46505 + r46508;
        return r46509;
}

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 2019347 
(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))))