Average Error: 52.0 → 52.0
Time: 25.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r2575265 = 9.0;
        double r2575266 = x;
        double r2575267 = 4.0;
        double r2575268 = pow(r2575266, r2575267);
        double r2575269 = r2575265 * r2575268;
        double r2575270 = y;
        double r2575271 = pow(r2575270, r2575267);
        double r2575272 = r2575269 - r2575271;
        double r2575273 = 2.0;
        double r2575274 = r2575270 * r2575270;
        double r2575275 = r2575273 * r2575274;
        double r2575276 = r2575272 + r2575275;
        return r2575276;
}
↓
double f(double x, double y) {
        double r2575277 = 2.0;
        double r2575278 = y;
        double r2575279 = r2575278 * r2575278;
        double r2575280 = r2575277 * r2575279;
        double r2575281 = x;
        double r2575282 = 4.0;
        double r2575283 = pow(r2575281, r2575282);
        double r2575284 = 9.0;
        double r2575285 = r2575283 * r2575284;
        double r2575286 = pow(r2575278, r2575282);
        double r2575287 = r2575285 - r2575286;
        double r2575288 = r2575287 * r2575287;
        double r2575289 = r2575287 * r2575288;
        double r2575290 = cbrt(r2575289);
        double r2575291 = r2575280 + r2575290;
        return r2575291;
}

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

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

Reproduce

herbie shell --seed 2019168 +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))))