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 r79016 = 9.0;
        double r79017 = x;
        double r79018 = 4.0;
        double r79019 = pow(r79017, r79018);
        double r79020 = r79016 * r79019;
        double r79021 = y;
        double r79022 = pow(r79021, r79018);
        double r79023 = r79020 - r79022;
        double r79024 = 2.0;
        double r79025 = r79021 * r79021;
        double r79026 = r79024 * r79025;
        double r79027 = r79023 + r79026;
        return r79027;
}
↓
double f(double x, double y) {
        double r79028 = 9.0;
        double r79029 = x;
        double r79030 = 4.0;
        double r79031 = pow(r79029, r79030);
        double r79032 = r79028 * r79031;
        double r79033 = y;
        double r79034 = pow(r79033, r79030);
        double r79035 = r79032 - r79034;
        double r79036 = 3.0;
        double r79037 = pow(r79035, r79036);
        double r79038 = cbrt(r79037);
        double r79039 = 2.0;
        double r79040 = r79033 * r79033;
        double r79041 = r79039 * r79040;
        double r79042 = r79038 + r79041;
        return r79042;
}

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))))