Average Error: 52.0 → 52.0
Time: 8.2s
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 r94676 = 9.0;
        double r94677 = x;
        double r94678 = 4.0;
        double r94679 = pow(r94677, r94678);
        double r94680 = r94676 * r94679;
        double r94681 = y;
        double r94682 = pow(r94681, r94678);
        double r94683 = r94680 - r94682;
        double r94684 = 2.0;
        double r94685 = r94681 * r94681;
        double r94686 = r94684 * r94685;
        double r94687 = r94683 + r94686;
        return r94687;
}
↓
double f(double x, double y) {
        double r94688 = 9.0;
        double r94689 = x;
        double r94690 = 4.0;
        double r94691 = pow(r94689, r94690);
        double r94692 = r94688 * r94691;
        double r94693 = y;
        double r94694 = pow(r94693, r94690);
        double r94695 = r94692 - r94694;
        double r94696 = 3.0;
        double r94697 = pow(r94695, r94696);
        double r94698 = cbrt(r94697);
        double r94699 = 2.0;
        double r94700 = r94693 * r94693;
        double r94701 = r94699 * r94700;
        double r94702 = r94698 + r94701;
        return r94702;
}

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 2019351 
(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))))