Average Error: 52.0 → 52.0
Time: 7.4s
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 r58676 = 9.0;
        double r58677 = x;
        double r58678 = 4.0;
        double r58679 = pow(r58677, r58678);
        double r58680 = r58676 * r58679;
        double r58681 = y;
        double r58682 = pow(r58681, r58678);
        double r58683 = r58680 - r58682;
        double r58684 = 2.0;
        double r58685 = r58681 * r58681;
        double r58686 = r58684 * r58685;
        double r58687 = r58683 + r58686;
        return r58687;
}
↓
double f(double x, double y) {
        double r58688 = 9.0;
        double r58689 = x;
        double r58690 = 4.0;
        double r58691 = pow(r58689, r58690);
        double r58692 = r58688 * r58691;
        double r58693 = y;
        double r58694 = pow(r58693, r58690);
        double r58695 = r58692 - r58694;
        double r58696 = 3.0;
        double r58697 = pow(r58695, r58696);
        double r58698 = cbrt(r58697);
        double r58699 = 2.0;
        double r58700 = r58693 * r58693;
        double r58701 = r58699 * r58700;
        double r58702 = r58698 + r58701;
        return r58702;
}

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 2019198 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))