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 r56288 = 9.0;
        double r56289 = x;
        double r56290 = 4.0;
        double r56291 = pow(r56289, r56290);
        double r56292 = r56288 * r56291;
        double r56293 = y;
        double r56294 = pow(r56293, r56290);
        double r56295 = r56292 - r56294;
        double r56296 = 2.0;
        double r56297 = r56293 * r56293;
        double r56298 = r56296 * r56297;
        double r56299 = r56295 + r56298;
        return r56299;
}
↓
double f(double x, double y) {
        double r56300 = 9.0;
        double r56301 = x;
        double r56302 = 4.0;
        double r56303 = pow(r56301, r56302);
        double r56304 = r56300 * r56303;
        double r56305 = y;
        double r56306 = pow(r56305, r56302);
        double r56307 = r56304 - r56306;
        double r56308 = 3.0;
        double r56309 = pow(r56307, r56308);
        double r56310 = cbrt(r56309);
        double r56311 = 2.0;
        double r56312 = r56305 * r56305;
        double r56313 = r56311 * r56312;
        double r56314 = r56310 + r56313;
        return r56314;
}

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 2020049 
(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))))