Average Error: 52.0 → 52.0
Time: 20.5s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{\left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{\left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r2951259 = 9.0;
        double r2951260 = x;
        double r2951261 = 4.0;
        double r2951262 = pow(r2951260, r2951261);
        double r2951263 = r2951259 * r2951262;
        double r2951264 = y;
        double r2951265 = pow(r2951264, r2951261);
        double r2951266 = r2951263 - r2951265;
        double r2951267 = 2.0;
        double r2951268 = r2951264 * r2951264;
        double r2951269 = r2951267 * r2951268;
        double r2951270 = r2951266 + r2951269;
        return r2951270;
}
↓
double f(double x, double y) {
        double r2951271 = x;
        double r2951272 = 4.0;
        double r2951273 = pow(r2951271, r2951272);
        double r2951274 = 9.0;
        double r2951275 = r2951273 * r2951274;
        double r2951276 = y;
        double r2951277 = pow(r2951276, r2951272);
        double r2951278 = r2951275 - r2951277;
        double r2951279 = r2951278 * r2951278;
        double r2951280 = r2951279 * r2951278;
        double r2951281 = cbrt(r2951280);
        double r2951282 = 2.0;
        double r2951283 = r2951276 * r2951276;
        double r2951284 = r2951282 * r2951283;
        double r2951285 = r2951281 + r2951284;
        return r2951285;
}

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. Final simplification52.0

    \[\leadsto \sqrt[3]{\left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)} + 2 \cdot \left(y \cdot y\right)\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))