Average Error: 52.0 → 52.0
Time: 2.8s
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 r72005 = 9.0;
        double r72006 = x;
        double r72007 = 4.0;
        double r72008 = pow(r72006, r72007);
        double r72009 = r72005 * r72008;
        double r72010 = y;
        double r72011 = pow(r72010, r72007);
        double r72012 = r72009 - r72011;
        double r72013 = 2.0;
        double r72014 = r72010 * r72010;
        double r72015 = r72013 * r72014;
        double r72016 = r72012 + r72015;
        return r72016;
}
↓
double f(double x, double y) {
        double r72017 = 9.0;
        double r72018 = x;
        double r72019 = 4.0;
        double r72020 = pow(r72018, r72019);
        double r72021 = r72017 * r72020;
        double r72022 = y;
        double r72023 = pow(r72022, r72019);
        double r72024 = r72021 - r72023;
        double r72025 = 3.0;
        double r72026 = pow(r72024, r72025);
        double r72027 = cbrt(r72026);
        double r72028 = 2.0;
        double r72029 = r72022 * r72022;
        double r72030 = r72028 * r72029;
        double r72031 = r72027 + r72030;
        return r72031;
}

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 2020036 
(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))))