Average Error: 62.0 → 62.0
Time: 4.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[9 \cdot {x}^{4} - \left({y}^{4} - 2 \cdot \left(y \cdot y\right)\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
9 \cdot {x}^{4} - \left({y}^{4} - 2 \cdot \left(y \cdot y\right)\right)
double f(double x, double y) {
        double r50979 = 9.0;
        double r50980 = x;
        double r50981 = 4.0;
        double r50982 = pow(r50980, r50981);
        double r50983 = r50979 * r50982;
        double r50984 = y;
        double r50985 = r50984 * r50984;
        double r50986 = 2.0;
        double r50987 = r50985 - r50986;
        double r50988 = r50985 * r50987;
        double r50989 = r50983 - r50988;
        return r50989;
}
↓
double f(double x, double y) {
        double r50990 = 9.0;
        double r50991 = x;
        double r50992 = 4.0;
        double r50993 = pow(r50991, r50992);
        double r50994 = r50990 * r50993;
        double r50995 = y;
        double r50996 = 4.0;
        double r50997 = pow(r50995, r50996);
        double r50998 = 2.0;
        double r50999 = r50995 * r50995;
        double r51000 = r50998 * r50999;
        double r51001 = r50997 - r51000;
        double r51002 = r50994 - r51001;
        return r51002;
}

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

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

  8. Applied add-cbrt-cube52.0

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

  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 simplification62.0

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

Reproduce

herbie shell --seed 2019304 
(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))))