Average Error: 52.0 → 52.0
Time: 2.4s
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 r52822 = 9.0;
        double r52823 = x;
        double r52824 = 4.0;
        double r52825 = pow(r52823, r52824);
        double r52826 = r52822 * r52825;
        double r52827 = y;
        double r52828 = pow(r52827, r52824);
        double r52829 = r52826 - r52828;
        double r52830 = 2.0;
        double r52831 = r52827 * r52827;
        double r52832 = r52830 * r52831;
        double r52833 = r52829 + r52832;
        return r52833;
}
↓
double f(double x, double y) {
        double r52834 = 9.0;
        double r52835 = x;
        double r52836 = 4.0;
        double r52837 = pow(r52835, r52836);
        double r52838 = r52834 * r52837;
        double r52839 = y;
        double r52840 = pow(r52839, r52836);
        double r52841 = r52838 - r52840;
        double r52842 = 3.0;
        double r52843 = pow(r52841, r52842);
        double r52844 = cbrt(r52843);
        double r52845 = 2.0;
        double r52846 = r52839 * r52839;
        double r52847 = r52845 * r52846;
        double r52848 = r52844 + r52847;
        return r52848;
}

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 2020036 
(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))))