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 r59611 = 9.0;
        double r59612 = x;
        double r59613 = 4.0;
        double r59614 = pow(r59612, r59613);
        double r59615 = r59611 * r59614;
        double r59616 = y;
        double r59617 = pow(r59616, r59613);
        double r59618 = r59615 - r59617;
        double r59619 = 2.0;
        double r59620 = r59616 * r59616;
        double r59621 = r59619 * r59620;
        double r59622 = r59618 + r59621;
        return r59622;
}
↓
double f(double x, double y) {
        double r59623 = 9.0;
        double r59624 = x;
        double r59625 = 4.0;
        double r59626 = pow(r59624, r59625);
        double r59627 = r59623 * r59626;
        double r59628 = y;
        double r59629 = pow(r59628, r59625);
        double r59630 = r59627 - r59629;
        double r59631 = 3.0;
        double r59632 = pow(r59630, r59631);
        double r59633 = cbrt(r59632);
        double r59634 = 2.0;
        double r59635 = r59628 * r59628;
        double r59636 = r59634 * r59635;
        double r59637 = r59633 + r59636;
        return r59637;
}

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 2019354 
(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))))