Average Error: 52.0 → 52.0
Time: 2.6s
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 r41384 = 9.0;
        double r41385 = x;
        double r41386 = 4.0;
        double r41387 = pow(r41385, r41386);
        double r41388 = r41384 * r41387;
        double r41389 = y;
        double r41390 = pow(r41389, r41386);
        double r41391 = r41388 - r41390;
        double r41392 = 2.0;
        double r41393 = r41389 * r41389;
        double r41394 = r41392 * r41393;
        double r41395 = r41391 + r41394;
        return r41395;
}
↓
double f(double x, double y) {
        double r41396 = 9.0;
        double r41397 = x;
        double r41398 = 4.0;
        double r41399 = pow(r41397, r41398);
        double r41400 = r41396 * r41399;
        double r41401 = y;
        double r41402 = pow(r41401, r41398);
        double r41403 = r41400 - r41402;
        double r41404 = 3.0;
        double r41405 = pow(r41403, r41404);
        double r41406 = cbrt(r41405);
        double r41407 = 2.0;
        double r41408 = r41401 * r41401;
        double r41409 = r41407 * r41408;
        double r41410 = r41406 + r41409;
        return r41410;
}

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 2020100 +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))))