Average Error: 52.0 → 52.0
Time: 3.0s
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 r59359 = 9.0;
        double r59360 = x;
        double r59361 = 4.0;
        double r59362 = pow(r59360, r59361);
        double r59363 = r59359 * r59362;
        double r59364 = y;
        double r59365 = pow(r59364, r59361);
        double r59366 = r59363 - r59365;
        double r59367 = 2.0;
        double r59368 = r59364 * r59364;
        double r59369 = r59367 * r59368;
        double r59370 = r59366 + r59369;
        return r59370;
}
↓
double f(double x, double y) {
        double r59371 = 9.0;
        double r59372 = x;
        double r59373 = 4.0;
        double r59374 = pow(r59372, r59373);
        double r59375 = r59371 * r59374;
        double r59376 = y;
        double r59377 = pow(r59376, r59373);
        double r59378 = r59375 - r59377;
        double r59379 = 3.0;
        double r59380 = pow(r59378, r59379);
        double r59381 = cbrt(r59380);
        double r59382 = 2.0;
        double r59383 = r59376 * r59376;
        double r59384 = r59382 * r59383;
        double r59385 = r59381 + r59384;
        return r59385;
}

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 2019322 
(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))))