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 r65106 = 9.0;
        double r65107 = x;
        double r65108 = 4.0;
        double r65109 = pow(r65107, r65108);
        double r65110 = r65106 * r65109;
        double r65111 = y;
        double r65112 = pow(r65111, r65108);
        double r65113 = r65110 - r65112;
        double r65114 = 2.0;
        double r65115 = r65111 * r65111;
        double r65116 = r65114 * r65115;
        double r65117 = r65113 + r65116;
        return r65117;
}
↓
double f(double x, double y) {
        double r65118 = 9.0;
        double r65119 = x;
        double r65120 = 4.0;
        double r65121 = pow(r65119, r65120);
        double r65122 = r65118 * r65121;
        double r65123 = y;
        double r65124 = pow(r65123, r65120);
        double r65125 = r65122 - r65124;
        double r65126 = 3.0;
        double r65127 = pow(r65125, r65126);
        double r65128 = cbrt(r65127);
        double r65129 = 2.0;
        double r65130 = r65123 * r65123;
        double r65131 = r65129 * r65130;
        double r65132 = r65128 + r65131;
        return r65132;
}

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 2019362 
(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))))