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 r57214 = 9.0;
        double r57215 = x;
        double r57216 = 4.0;
        double r57217 = pow(r57215, r57216);
        double r57218 = r57214 * r57217;
        double r57219 = y;
        double r57220 = pow(r57219, r57216);
        double r57221 = r57218 - r57220;
        double r57222 = 2.0;
        double r57223 = r57219 * r57219;
        double r57224 = r57222 * r57223;
        double r57225 = r57221 + r57224;
        return r57225;
}
↓
double f(double x, double y) {
        double r57226 = 9.0;
        double r57227 = x;
        double r57228 = 4.0;
        double r57229 = pow(r57227, r57228);
        double r57230 = r57226 * r57229;
        double r57231 = y;
        double r57232 = pow(r57231, r57228);
        double r57233 = r57230 - r57232;
        double r57234 = 3.0;
        double r57235 = pow(r57233, r57234);
        double r57236 = cbrt(r57235);
        double r57237 = 2.0;
        double r57238 = r57231 * r57231;
        double r57239 = r57237 * r57238;
        double r57240 = r57236 + r57239;
        return r57240;
}

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 2019353 
(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))))