Average Error: 52.0 → 52.0
Time: 4.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)
double f(double x, double y) {
        double r42877 = 9.0;
        double r42878 = x;
        double r42879 = 4.0;
        double r42880 = pow(r42878, r42879);
        double r42881 = r42877 * r42880;
        double r42882 = y;
        double r42883 = pow(r42882, r42879);
        double r42884 = r42881 - r42883;
        double r42885 = 2.0;
        double r42886 = r42882 * r42882;
        double r42887 = r42885 * r42886;
        double r42888 = r42884 + r42887;
        return r42888;
}
↓
double f(double x, double y) {
        double r42889 = 2.0;
        double r42890 = y;
        double r42891 = r42890 * r42890;
        double r42892 = r42889 * r42891;
        double r42893 = 9.0;
        double r42894 = x;
        double r42895 = 4.0;
        double r42896 = pow(r42894, r42895);
        double r42897 = r42893 * r42896;
        double r42898 = pow(r42890, r42895);
        double r42899 = r42897 - r42898;
        double r42900 = r42892 + r42899;
        return r42900;
}

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

    \[\leadsto 2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]

Reproduce

herbie shell --seed 2019304 
(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))))