Average Error: 62.0 → 52.0
Time: 3.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)
double f(double x, double y) {
        double r58437 = 9.0;
        double r58438 = x;
        double r58439 = 4.0;
        double r58440 = pow(r58438, r58439);
        double r58441 = r58437 * r58440;
        double r58442 = y;
        double r58443 = r58442 * r58442;
        double r58444 = 2.0;
        double r58445 = r58443 - r58444;
        double r58446 = r58443 * r58445;
        double r58447 = r58441 - r58446;
        return r58447;
}
↓
double f(double x, double y) {
        double r58448 = 9.0;
        double r58449 = x;
        double r58450 = 4.0;
        double r58451 = pow(r58449, r58450);
        double r58452 = r58448 * r58451;
        double r58453 = y;
        double r58454 = 4.0;
        double r58455 = pow(r58453, r58454);
        double r58456 = r58452 - r58455;
        double r58457 = 3.0;
        double r58458 = pow(r58456, r58457);
        double r58459 = cbrt(r58458);
        double r58460 = r58453 * r58453;
        double r58461 = 2.0;
        double r58462 = -r58461;
        double r58463 = r58460 * r58462;
        double r58464 = r58459 - r58463;
        return r58464;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg62.0

    \[\leadsto 9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot y + \left(-2\right)\right)}\]

  4. Applied distribute-lft-in62.0

    \[\leadsto 9 \cdot {x}^{4} - \color{blue}{\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right) + \left(y \cdot y\right) \cdot \left(-2\right)\right)}\]

  5. Applied associate--r+52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) - \left(y \cdot y\right) \cdot \left(-2\right)}\]

  6. Simplified52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)} - \left(y \cdot y\right) \cdot \left(-2\right)\]
  7. Using strategy rm

  8. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)\right) \cdot \left(9 \cdot {x}^{4} + \left(-{y}^{4}\right)\right)}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

  9. Simplified52.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

  10. Final simplification52.0

    \[\leadsto \sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (- (* 9 (pow x 4)) (* (* y y) (- (* y y) 2))))