Average Error: 52.0 → 52.0
Time: 2.4s
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 r56200 = 9.0;
        double r56201 = x;
        double r56202 = 4.0;
        double r56203 = pow(r56201, r56202);
        double r56204 = r56200 * r56203;
        double r56205 = y;
        double r56206 = pow(r56205, r56202);
        double r56207 = r56204 - r56206;
        double r56208 = 2.0;
        double r56209 = r56205 * r56205;
        double r56210 = r56208 * r56209;
        double r56211 = r56207 + r56210;
        return r56211;
}
↓
double f(double x, double y) {
        double r56212 = 9.0;
        double r56213 = x;
        double r56214 = 4.0;
        double r56215 = pow(r56213, r56214);
        double r56216 = r56212 * r56215;
        double r56217 = y;
        double r56218 = pow(r56217, r56214);
        double r56219 = r56216 - r56218;
        double r56220 = 3.0;
        double r56221 = pow(r56219, r56220);
        double r56222 = cbrt(r56221);
        double r56223 = 2.0;
        double r56224 = r56217 * r56217;
        double r56225 = r56223 * r56224;
        double r56226 = r56222 + r56225;
        return r56226;
}

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 2020062 
(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))))