Average Error: 52.0 → 52.0
Time: 7.9s
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 r113884 = 9.0;
        double r113885 = x;
        double r113886 = 4.0;
        double r113887 = pow(r113885, r113886);
        double r113888 = r113884 * r113887;
        double r113889 = y;
        double r113890 = pow(r113889, r113886);
        double r113891 = r113888 - r113890;
        double r113892 = 2.0;
        double r113893 = r113889 * r113889;
        double r113894 = r113892 * r113893;
        double r113895 = r113891 + r113894;
        return r113895;
}
↓
double f(double x, double y) {
        double r113896 = 9.0;
        double r113897 = x;
        double r113898 = 4.0;
        double r113899 = pow(r113897, r113898);
        double r113900 = r113896 * r113899;
        double r113901 = y;
        double r113902 = pow(r113901, r113898);
        double r113903 = r113900 - r113902;
        double r113904 = 3.0;
        double r113905 = pow(r113903, r113904);
        double r113906 = cbrt(r113905);
        double r113907 = 2.0;
        double r113908 = r113901 * r113901;
        double r113909 = r113907 * r113908;
        double r113910 = r113906 + r113909;
        return r113910;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2020043 
(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))))