Average Error: 62.0 → 52.0
Time: 11.5s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(-2\right) \cdot \left(y \cdot y\right)\]
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(-2\right) \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r56480 = 9.0;
        double r56481 = x;
        double r56482 = 4.0;
        double r56483 = pow(r56481, r56482);
        double r56484 = r56480 * r56483;
        double r56485 = y;
        double r56486 = r56485 * r56485;
        double r56487 = 2.0;
        double r56488 = r56486 - r56487;
        double r56489 = r56486 * r56488;
        double r56490 = r56484 - r56489;
        return r56490;
}
↓
double f(double x, double y) {
        double r56491 = 9.0;
        double r56492 = x;
        double r56493 = 4.0;
        double r56494 = pow(r56492, r56493);
        double r56495 = r56491 * r56494;
        double r56496 = y;
        double r56497 = 4.0;
        double r56498 = pow(r56496, r56497);
        double r56499 = r56495 - r56498;
        double r56500 = 3.0;
        double r56501 = pow(r56499, r56500);
        double r56502 = cbrt(r56501);
        double r56503 = 2.0;
        double r56504 = -r56503;
        double r56505 = r56496 * r56496;
        double r56506 = r56504 * r56505;
        double r56507 = r56502 - r56506;
        return r56507;
}

Error

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Your Program's Arguments

Results

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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-rgt-in62.0

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

  5. Applied associate--r+52.0

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

  6. Simplified52.0

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

  8. Applied add-cbrt-cube52.0

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

  9. Simplified52.0

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

  10. Final simplification52.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))