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 r54680 = 9.0;
        double r54681 = x;
        double r54682 = 4.0;
        double r54683 = pow(r54681, r54682);
        double r54684 = r54680 * r54683;
        double r54685 = y;
        double r54686 = pow(r54685, r54682);
        double r54687 = r54684 - r54686;
        double r54688 = 2.0;
        double r54689 = r54685 * r54685;
        double r54690 = r54688 * r54689;
        double r54691 = r54687 + r54690;
        return r54691;
}
↓
double f(double x, double y) {
        double r54692 = 9.0;
        double r54693 = x;
        double r54694 = 4.0;
        double r54695 = pow(r54693, r54694);
        double r54696 = r54692 * r54695;
        double r54697 = y;
        double r54698 = pow(r54697, r54694);
        double r54699 = r54696 - r54698;
        double r54700 = 3.0;
        double r54701 = pow(r54699, r54700);
        double r54702 = cbrt(r54701);
        double r54703 = 2.0;
        double r54704 = r54697 * r54697;
        double r54705 = r54703 * r54704;
        double r54706 = r54702 + r54705;
        return r54706;
}

Error

Try it out

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 2020056 +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))))