Average Error: 52.0 → 52.0
Time: 2.4s
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 r51570 = 9.0;
        double r51571 = x;
        double r51572 = 4.0;
        double r51573 = pow(r51571, r51572);
        double r51574 = r51570 * r51573;
        double r51575 = y;
        double r51576 = pow(r51575, r51572);
        double r51577 = r51574 - r51576;
        double r51578 = 2.0;
        double r51579 = r51575 * r51575;
        double r51580 = r51578 * r51579;
        double r51581 = r51577 + r51580;
        return r51581;
}
↓
double f(double x, double y) {
        double r51582 = 9.0;
        double r51583 = x;
        double r51584 = 4.0;
        double r51585 = pow(r51583, r51584);
        double r51586 = r51582 * r51585;
        double r51587 = y;
        double r51588 = pow(r51587, r51584);
        double r51589 = r51586 - r51588;
        double r51590 = 3.0;
        double r51591 = pow(r51589, r51590);
        double r51592 = cbrt(r51591);
        double r51593 = 2.0;
        double r51594 = r51587 * r51587;
        double r51595 = r51593 * r51594;
        double r51596 = r51592 + r51595;
        return r51596;
}

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 2020018 
(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))))