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 r51462 = 9.0;
        double r51463 = x;
        double r51464 = 4.0;
        double r51465 = pow(r51463, r51464);
        double r51466 = r51462 * r51465;
        double r51467 = y;
        double r51468 = pow(r51467, r51464);
        double r51469 = r51466 - r51468;
        double r51470 = 2.0;
        double r51471 = r51467 * r51467;
        double r51472 = r51470 * r51471;
        double r51473 = r51469 + r51472;
        return r51473;
}
↓
double f(double x, double y) {
        double r51474 = 9.0;
        double r51475 = x;
        double r51476 = 4.0;
        double r51477 = pow(r51475, r51476);
        double r51478 = r51474 * r51477;
        double r51479 = y;
        double r51480 = pow(r51479, r51476);
        double r51481 = r51478 - r51480;
        double r51482 = 3.0;
        double r51483 = pow(r51481, r51482);
        double r51484 = cbrt(r51483);
        double r51485 = 2.0;
        double r51486 = r51479 * r51479;
        double r51487 = r51485 * r51486;
        double r51488 = r51484 + r51487;
        return r51488;
}

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 2020100 
(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))))