Average Error: 52.0 → 52.0
Time: 5.4s
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 r52524 = 9.0;
        double r52525 = x;
        double r52526 = 4.0;
        double r52527 = pow(r52525, r52526);
        double r52528 = r52524 * r52527;
        double r52529 = y;
        double r52530 = pow(r52529, r52526);
        double r52531 = r52528 - r52530;
        double r52532 = 2.0;
        double r52533 = r52529 * r52529;
        double r52534 = r52532 * r52533;
        double r52535 = r52531 + r52534;
        return r52535;
}
↓
double f(double x, double y) {
        double r52536 = 9.0;
        double r52537 = x;
        double r52538 = 4.0;
        double r52539 = pow(r52537, r52538);
        double r52540 = r52536 * r52539;
        double r52541 = y;
        double r52542 = pow(r52541, r52538);
        double r52543 = r52540 - r52542;
        double r52544 = 3.0;
        double r52545 = pow(r52543, r52544);
        double r52546 = cbrt(r52545);
        double r52547 = 2.0;
        double r52548 = r52541 * r52541;
        double r52549 = r52547 * r52548;
        double r52550 = r52546 + r52549;
        return r52550;
}

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 2020046 
(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))))