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 r87238 = 9.0;
        double r87239 = x;
        double r87240 = 4.0;
        double r87241 = pow(r87239, r87240);
        double r87242 = r87238 * r87241;
        double r87243 = y;
        double r87244 = pow(r87243, r87240);
        double r87245 = r87242 - r87244;
        double r87246 = 2.0;
        double r87247 = r87243 * r87243;
        double r87248 = r87246 * r87247;
        double r87249 = r87245 + r87248;
        return r87249;
}
↓
double f(double x, double y) {
        double r87250 = 9.0;
        double r87251 = x;
        double r87252 = 4.0;
        double r87253 = pow(r87251, r87252);
        double r87254 = r87250 * r87253;
        double r87255 = y;
        double r87256 = pow(r87255, r87252);
        double r87257 = r87254 - r87256;
        double r87258 = 3.0;
        double r87259 = pow(r87257, r87258);
        double r87260 = cbrt(r87259);
        double r87261 = 2.0;
        double r87262 = r87255 * r87255;
        double r87263 = r87261 * r87262;
        double r87264 = r87260 + r87263;
        return r87264;
}

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 2020001 +o rules:numerics
(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))))