Average Error: 52.0 → 52.0
Time: 2.7s
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 r67746 = 9.0;
        double r67747 = x;
        double r67748 = 4.0;
        double r67749 = pow(r67747, r67748);
        double r67750 = r67746 * r67749;
        double r67751 = y;
        double r67752 = pow(r67751, r67748);
        double r67753 = r67750 - r67752;
        double r67754 = 2.0;
        double r67755 = r67751 * r67751;
        double r67756 = r67754 * r67755;
        double r67757 = r67753 + r67756;
        return r67757;
}
↓
double f(double x, double y) {
        double r67758 = 9.0;
        double r67759 = x;
        double r67760 = 4.0;
        double r67761 = pow(r67759, r67760);
        double r67762 = r67758 * r67761;
        double r67763 = y;
        double r67764 = pow(r67763, r67760);
        double r67765 = r67762 - r67764;
        double r67766 = 3.0;
        double r67767 = pow(r67765, r67766);
        double r67768 = cbrt(r67767);
        double r67769 = 2.0;
        double r67770 = r67763 * r67763;
        double r67771 = r67769 * r67770;
        double r67772 = r67768 + r67771;
        return r67772;
}

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 2020064 
(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))))