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 r71383 = 9.0;
        double r71384 = x;
        double r71385 = 4.0;
        double r71386 = pow(r71384, r71385);
        double r71387 = r71383 * r71386;
        double r71388 = y;
        double r71389 = pow(r71388, r71385);
        double r71390 = r71387 - r71389;
        double r71391 = 2.0;
        double r71392 = r71388 * r71388;
        double r71393 = r71391 * r71392;
        double r71394 = r71390 + r71393;
        return r71394;
}
↓
double f(double x, double y) {
        double r71395 = 9.0;
        double r71396 = x;
        double r71397 = 4.0;
        double r71398 = pow(r71396, r71397);
        double r71399 = r71395 * r71398;
        double r71400 = y;
        double r71401 = pow(r71400, r71397);
        double r71402 = r71399 - r71401;
        double r71403 = 3.0;
        double r71404 = pow(r71402, r71403);
        double r71405 = cbrt(r71404);
        double r71406 = 2.0;
        double r71407 = r71400 * r71400;
        double r71408 = r71406 * r71407;
        double r71409 = r71405 + r71408;
        return r71409;
}

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 2020025 
(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))))