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 r52007 = 9.0;
        double r52008 = x;
        double r52009 = 4.0;
        double r52010 = pow(r52008, r52009);
        double r52011 = r52007 * r52010;
        double r52012 = y;
        double r52013 = pow(r52012, r52009);
        double r52014 = r52011 - r52013;
        double r52015 = 2.0;
        double r52016 = r52012 * r52012;
        double r52017 = r52015 * r52016;
        double r52018 = r52014 + r52017;
        return r52018;
}
↓
double f(double x, double y) {
        double r52019 = 9.0;
        double r52020 = x;
        double r52021 = 4.0;
        double r52022 = pow(r52020, r52021);
        double r52023 = r52019 * r52022;
        double r52024 = y;
        double r52025 = pow(r52024, r52021);
        double r52026 = r52023 - r52025;
        double r52027 = 3.0;
        double r52028 = pow(r52026, r52027);
        double r52029 = cbrt(r52028);
        double r52030 = 2.0;
        double r52031 = r52024 * r52024;
        double r52032 = r52030 * r52031;
        double r52033 = r52029 + r52032;
        return r52033;
}

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 2020021 
(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))))