Average Error: 52.0 → 52.0
Time: 2.6s
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 r72785 = 9.0;
        double r72786 = x;
        double r72787 = 4.0;
        double r72788 = pow(r72786, r72787);
        double r72789 = r72785 * r72788;
        double r72790 = y;
        double r72791 = pow(r72790, r72787);
        double r72792 = r72789 - r72791;
        double r72793 = 2.0;
        double r72794 = r72790 * r72790;
        double r72795 = r72793 * r72794;
        double r72796 = r72792 + r72795;
        return r72796;
}
↓
double f(double x, double y) {
        double r72797 = 9.0;
        double r72798 = x;
        double r72799 = 4.0;
        double r72800 = pow(r72798, r72799);
        double r72801 = r72797 * r72800;
        double r72802 = y;
        double r72803 = pow(r72802, r72799);
        double r72804 = r72801 - r72803;
        double r72805 = 3.0;
        double r72806 = pow(r72804, r72805);
        double r72807 = cbrt(r72806);
        double r72808 = 2.0;
        double r72809 = r72802 * r72802;
        double r72810 = r72808 * r72809;
        double r72811 = r72807 + r72810;
        return r72811;
}

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 2019353 +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))))