Average Error: 52.0 → 52.0
Time: 7.2s
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 r64778 = 9.0;
        double r64779 = x;
        double r64780 = 4.0;
        double r64781 = pow(r64779, r64780);
        double r64782 = r64778 * r64781;
        double r64783 = y;
        double r64784 = pow(r64783, r64780);
        double r64785 = r64782 - r64784;
        double r64786 = 2.0;
        double r64787 = r64783 * r64783;
        double r64788 = r64786 * r64787;
        double r64789 = r64785 + r64788;
        return r64789;
}
↓
double f(double x, double y) {
        double r64790 = 9.0;
        double r64791 = x;
        double r64792 = 4.0;
        double r64793 = pow(r64791, r64792);
        double r64794 = r64790 * r64793;
        double r64795 = y;
        double r64796 = pow(r64795, r64792);
        double r64797 = r64794 - r64796;
        double r64798 = 3.0;
        double r64799 = pow(r64797, r64798);
        double r64800 = cbrt(r64799);
        double r64801 = 2.0;
        double r64802 = r64795 * r64795;
        double r64803 = r64801 * r64802;
        double r64804 = r64800 + r64803;
        return r64804;
}

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 2020042 
(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))))