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 r70332 = 9.0;
        double r70333 = x;
        double r70334 = 4.0;
        double r70335 = pow(r70333, r70334);
        double r70336 = r70332 * r70335;
        double r70337 = y;
        double r70338 = pow(r70337, r70334);
        double r70339 = r70336 - r70338;
        double r70340 = 2.0;
        double r70341 = r70337 * r70337;
        double r70342 = r70340 * r70341;
        double r70343 = r70339 + r70342;
        return r70343;
}
↓
double f(double x, double y) {
        double r70344 = 9.0;
        double r70345 = x;
        double r70346 = 4.0;
        double r70347 = pow(r70345, r70346);
        double r70348 = r70344 * r70347;
        double r70349 = y;
        double r70350 = pow(r70349, r70346);
        double r70351 = r70348 - r70350;
        double r70352 = 3.0;
        double r70353 = pow(r70351, r70352);
        double r70354 = cbrt(r70353);
        double r70355 = 2.0;
        double r70356 = r70349 * r70349;
        double r70357 = r70355 * r70356;
        double r70358 = r70354 + r70357;
        return r70358;
}

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 2020003 
(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))))