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 r44178 = 9.0;
        double r44179 = x;
        double r44180 = 4.0;
        double r44181 = pow(r44179, r44180);
        double r44182 = r44178 * r44181;
        double r44183 = y;
        double r44184 = pow(r44183, r44180);
        double r44185 = r44182 - r44184;
        double r44186 = 2.0;
        double r44187 = r44183 * r44183;
        double r44188 = r44186 * r44187;
        double r44189 = r44185 + r44188;
        return r44189;
}
↓
double f(double x, double y) {
        double r44190 = 9.0;
        double r44191 = x;
        double r44192 = 4.0;
        double r44193 = pow(r44191, r44192);
        double r44194 = r44190 * r44193;
        double r44195 = y;
        double r44196 = pow(r44195, r44192);
        double r44197 = r44194 - r44196;
        double r44198 = 3.0;
        double r44199 = pow(r44197, r44198);
        double r44200 = cbrt(r44199);
        double r44201 = 2.0;
        double r44202 = r44195 * r44195;
        double r44203 = r44201 * r44202;
        double r44204 = r44200 + r44203;
        return r44204;
}

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 2020047 
(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))))