Average Error: 52.0 → 52.0
Time: 13.1s
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 r42763 = 9.0;
        double r42764 = x;
        double r42765 = 4.0;
        double r42766 = pow(r42764, r42765);
        double r42767 = r42763 * r42766;
        double r42768 = y;
        double r42769 = pow(r42768, r42765);
        double r42770 = r42767 - r42769;
        double r42771 = 2.0;
        double r42772 = r42768 * r42768;
        double r42773 = r42771 * r42772;
        double r42774 = r42770 + r42773;
        return r42774;
}
↓
double f(double x, double y) {
        double r42775 = 9.0;
        double r42776 = x;
        double r42777 = 4.0;
        double r42778 = pow(r42776, r42777);
        double r42779 = r42775 * r42778;
        double r42780 = y;
        double r42781 = pow(r42780, r42777);
        double r42782 = r42779 - r42781;
        double r42783 = 3.0;
        double r42784 = pow(r42782, r42783);
        double r42785 = cbrt(r42784);
        double r42786 = 2.0;
        double r42787 = r42780 * r42780;
        double r42788 = r42786 * r42787;
        double r42789 = r42785 + r42788;
        return r42789;
}

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 2019323 
(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))))