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 r69823 = 9.0;
        double r69824 = x;
        double r69825 = 4.0;
        double r69826 = pow(r69824, r69825);
        double r69827 = r69823 * r69826;
        double r69828 = y;
        double r69829 = pow(r69828, r69825);
        double r69830 = r69827 - r69829;
        double r69831 = 2.0;
        double r69832 = r69828 * r69828;
        double r69833 = r69831 * r69832;
        double r69834 = r69830 + r69833;
        return r69834;
}
↓
double f(double x, double y) {
        double r69835 = 9.0;
        double r69836 = x;
        double r69837 = 4.0;
        double r69838 = pow(r69836, r69837);
        double r69839 = r69835 * r69838;
        double r69840 = y;
        double r69841 = pow(r69840, r69837);
        double r69842 = r69839 - r69841;
        double r69843 = 3.0;
        double r69844 = pow(r69842, r69843);
        double r69845 = cbrt(r69844);
        double r69846 = 2.0;
        double r69847 = r69840 * r69840;
        double r69848 = r69846 * r69847;
        double r69849 = r69845 + r69848;
        return r69849;
}

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 2020064 +o rules:numerics
(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))))