Average Error: 52.0 → 52.0
Time: 2.5s
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 r65510 = 9.0;
        double r65511 = x;
        double r65512 = 4.0;
        double r65513 = pow(r65511, r65512);
        double r65514 = r65510 * r65513;
        double r65515 = y;
        double r65516 = pow(r65515, r65512);
        double r65517 = r65514 - r65516;
        double r65518 = 2.0;
        double r65519 = r65515 * r65515;
        double r65520 = r65518 * r65519;
        double r65521 = r65517 + r65520;
        return r65521;
}
↓
double f(double x, double y) {
        double r65522 = 9.0;
        double r65523 = x;
        double r65524 = 4.0;
        double r65525 = pow(r65523, r65524);
        double r65526 = r65522 * r65525;
        double r65527 = y;
        double r65528 = pow(r65527, r65524);
        double r65529 = r65526 - r65528;
        double r65530 = 3.0;
        double r65531 = pow(r65529, r65530);
        double r65532 = cbrt(r65531);
        double r65533 = 2.0;
        double r65534 = r65527 * r65527;
        double r65535 = r65533 * r65534;
        double r65536 = r65532 + r65535;
        return r65536;
}

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 2020020 +o rules:numerics
(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))))