Average Error: 62.0 → 62.0
Time: 11.9s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\left(\left(y \cdot y\right) \cdot 2 + 9 \cdot {x}^{4}\right) - {y}^{4}\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\left(\left(y \cdot y\right) \cdot 2 + 9 \cdot {x}^{4}\right) - {y}^{4}
double f(double x, double y) {
        double r43021 = 9.0;
        double r43022 = x;
        double r43023 = 4.0;
        double r43024 = pow(r43022, r43023);
        double r43025 = r43021 * r43024;
        double r43026 = y;
        double r43027 = r43026 * r43026;
        double r43028 = 2.0;
        double r43029 = r43027 - r43028;
        double r43030 = r43027 * r43029;
        double r43031 = r43025 - r43030;
        return r43031;
}
↓
double f(double x, double y) {
        double r43032 = y;
        double r43033 = r43032 * r43032;
        double r43034 = 2.0;
        double r43035 = r43033 * r43034;
        double r43036 = 9.0;
        double r43037 = x;
        double r43038 = 4.0;
        double r43039 = pow(r43037, r43038);
        double r43040 = r43036 * r43039;
        double r43041 = r43035 + r43040;
        double r43042 = 4.0;
        double r43043 = pow(r43032, r43042);
        double r43044 = r43041 - r43043;
        return r43044;
}

Error

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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-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. Using strategy rm

  7. Applied add-cbrt-cube52.0

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

  8. Simplified52.0

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

  9. Final simplification62.0

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

Reproduce

herbie shell --seed 2019294 
(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))))