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 r65412 = 9.0;
        double r65413 = x;
        double r65414 = 4.0;
        double r65415 = pow(r65413, r65414);
        double r65416 = r65412 * r65415;
        double r65417 = y;
        double r65418 = pow(r65417, r65414);
        double r65419 = r65416 - r65418;
        double r65420 = 2.0;
        double r65421 = r65417 * r65417;
        double r65422 = r65420 * r65421;
        double r65423 = r65419 + r65422;
        return r65423;
}
↓
double f(double x, double y) {
        double r65424 = 9.0;
        double r65425 = x;
        double r65426 = 4.0;
        double r65427 = pow(r65425, r65426);
        double r65428 = r65424 * r65427;
        double r65429 = y;
        double r65430 = pow(r65429, r65426);
        double r65431 = r65428 - r65430;
        double r65432 = 3.0;
        double r65433 = pow(r65431, r65432);
        double r65434 = cbrt(r65433);
        double r65435 = 2.0;
        double r65436 = r65429 * r65429;
        double r65437 = r65435 * r65436;
        double r65438 = r65434 + r65437;
        return r65438;
}

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 2020060 +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))))