Average Error: 52.0 → 52.0
Time: 6.6s
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 r67517 = 9.0;
        double r67518 = x;
        double r67519 = 4.0;
        double r67520 = pow(r67518, r67519);
        double r67521 = r67517 * r67520;
        double r67522 = y;
        double r67523 = pow(r67522, r67519);
        double r67524 = r67521 - r67523;
        double r67525 = 2.0;
        double r67526 = r67522 * r67522;
        double r67527 = r67525 * r67526;
        double r67528 = r67524 + r67527;
        return r67528;
}
↓
double f(double x, double y) {
        double r67529 = 9.0;
        double r67530 = x;
        double r67531 = 4.0;
        double r67532 = pow(r67530, r67531);
        double r67533 = r67529 * r67532;
        double r67534 = y;
        double r67535 = pow(r67534, r67531);
        double r67536 = r67533 - r67535;
        double r67537 = 3.0;
        double r67538 = pow(r67536, r67537);
        double r67539 = cbrt(r67538);
        double r67540 = 2.0;
        double r67541 = r67534 * r67534;
        double r67542 = r67540 * r67541;
        double r67543 = r67539 + r67542;
        return r67543;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2020045 
(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))))