Average Error: 52.0 → 52.0
Time: 2.5s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\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 r69305 = 9.0;
        double r69306 = x;
        double r69307 = 4.0;
        double r69308 = pow(r69306, r69307);
        double r69309 = r69305 * r69308;
        double r69310 = y;
        double r69311 = pow(r69310, r69307);
        double r69312 = r69309 - r69311;
        double r69313 = 2.0;
        double r69314 = r69310 * r69310;
        double r69315 = r69313 * r69314;
        double r69316 = r69312 + r69315;
        return r69316;
}
↓
double f(double x, double y) {
        double r69317 = 9.0;
        double r69318 = x;
        double r69319 = 4.0;
        double r69320 = pow(r69318, r69319);
        double r69321 = r69317 * r69320;
        double r69322 = y;
        double r69323 = pow(r69322, r69319);
        double r69324 = r69321 - r69323;
        double r69325 = 3.0;
        double r69326 = pow(r69324, r69325);
        double r69327 = cbrt(r69326);
        double r69328 = 2.0;
        double r69329 = r69322 * r69322;
        double r69330 = r69328 * r69329;
        double r69331 = r69327 + r69330;
        return r69331;
}

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 2020083 
(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))))