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 r36176 = 9.0;
        double r36177 = x;
        double r36178 = 4.0;
        double r36179 = pow(r36177, r36178);
        double r36180 = r36176 * r36179;
        double r36181 = y;
        double r36182 = r36181 * r36181;
        double r36183 = 2.0;
        double r36184 = r36182 - r36183;
        double r36185 = r36182 * r36184;
        double r36186 = r36180 - r36185;
        return r36186;
}
↓
double f(double x, double y) {
        double r36187 = y;
        double r36188 = r36187 * r36187;
        double r36189 = 2.0;
        double r36190 = r36188 * r36189;
        double r36191 = 9.0;
        double r36192 = x;
        double r36193 = 4.0;
        double r36194 = pow(r36192, r36193);
        double r36195 = r36191 * r36194;
        double r36196 = r36190 + r36195;
        double r36197 = 4.0;
        double r36198 = pow(r36187, r36197);
        double r36199 = r36196 - r36198;
        return r36199;
}

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 2019291 
(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))))