Average Error: 52.0 → 52.0
Time: 7.1s
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 r50568 = 9.0;
        double r50569 = x;
        double r50570 = 4.0;
        double r50571 = pow(r50569, r50570);
        double r50572 = r50568 * r50571;
        double r50573 = y;
        double r50574 = pow(r50573, r50570);
        double r50575 = r50572 - r50574;
        double r50576 = 2.0;
        double r50577 = r50573 * r50573;
        double r50578 = r50576 * r50577;
        double r50579 = r50575 + r50578;
        return r50579;
}
↓
double f(double x, double y) {
        double r50580 = 9.0;
        double r50581 = x;
        double r50582 = 4.0;
        double r50583 = pow(r50581, r50582);
        double r50584 = r50580 * r50583;
        double r50585 = y;
        double r50586 = pow(r50585, r50582);
        double r50587 = r50584 - r50586;
        double r50588 = 3.0;
        double r50589 = pow(r50587, r50588);
        double r50590 = cbrt(r50589);
        double r50591 = 2.0;
        double r50592 = r50585 * r50585;
        double r50593 = r50591 * r50592;
        double r50594 = r50590 + r50593;
        return r50594;
}

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 2019208 
(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))))