Average Error: 62.0 → 62.0
Time: 11.6s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\left(2 \cdot \left(y \cdot y\right) + 9 \cdot {x}^{4}\right) - {y}^{4}\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\left(2 \cdot \left(y \cdot y\right) + 9 \cdot {x}^{4}\right) - {y}^{4}
double f(double x, double y) {
        double r34225 = 9.0;
        double r34226 = x;
        double r34227 = 4.0;
        double r34228 = pow(r34226, r34227);
        double r34229 = r34225 * r34228;
        double r34230 = y;
        double r34231 = r34230 * r34230;
        double r34232 = 2.0;
        double r34233 = r34231 - r34232;
        double r34234 = r34231 * r34233;
        double r34235 = r34229 - r34234;
        return r34235;
}
↓
double f(double x, double y) {
        double r34236 = 2.0;
        double r34237 = y;
        double r34238 = r34237 * r34237;
        double r34239 = r34236 * r34238;
        double r34240 = 9.0;
        double r34241 = x;
        double r34242 = 4.0;
        double r34243 = pow(r34241, r34242);
        double r34244 = r34240 * r34243;
        double r34245 = r34239 + r34244;
        double r34246 = 4.0;
        double r34247 = pow(r34237, r34246);
        double r34248 = r34245 - r34247;
        return r34248;
}

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-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. Using strategy rm

  7. Applied add-cbrt-cube52.0

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

  8. Simplified52.0

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

  9. Final simplification62.0

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

Reproduce

herbie shell --seed 2019298 
(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))))