Average Error: 52.0 → 52.0
Time: 10.2s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)
double f(double x, double y) {
        double r42284 = 9.0;
        double r42285 = x;
        double r42286 = 4.0;
        double r42287 = pow(r42285, r42286);
        double r42288 = r42284 * r42287;
        double r42289 = y;
        double r42290 = pow(r42289, r42286);
        double r42291 = r42288 - r42290;
        double r42292 = 2.0;
        double r42293 = r42289 * r42289;
        double r42294 = r42292 * r42293;
        double r42295 = r42291 + r42294;
        return r42295;
}
↓
double f(double x, double y) {
        double r42296 = 2.0;
        double r42297 = y;
        double r42298 = r42297 * r42297;
        double r42299 = r42296 * r42298;
        double r42300 = 9.0;
        double r42301 = x;
        double r42302 = 4.0;
        double r42303 = pow(r42301, r42302);
        double r42304 = r42300 * r42303;
        double r42305 = pow(r42297, r42302);
        double r42306 = r42304 - r42305;
        double r42307 = r42299 + r42306;
        return r42307;
}

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

    \[\leadsto 2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]

Reproduce

herbie shell --seed 2019291 
(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))))