Average Error: 58.1 → 57.1
Time: 7.6s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[-2 \cdot {x}^{2} + \frac{x}{2 \cdot y}\]
\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}
↓
-2 \cdot {x}^{2} + \frac{x}{2 \cdot y}
double f(double x, double y) {
        double r19026 = 333.75;
        double r19027 = y;
        double r19028 = 6.0;
        double r19029 = pow(r19027, r19028);
        double r19030 = r19026 * r19029;
        double r19031 = x;
        double r19032 = r19031 * r19031;
        double r19033 = 11.0;
        double r19034 = r19033 * r19031;
        double r19035 = r19034 * r19031;
        double r19036 = r19035 * r19027;
        double r19037 = r19036 * r19027;
        double r19038 = r19037 - r19029;
        double r19039 = 121.0;
        double r19040 = 4.0;
        double r19041 = pow(r19027, r19040);
        double r19042 = r19039 * r19041;
        double r19043 = r19038 - r19042;
        double r19044 = 2.0;
        double r19045 = r19043 - r19044;
        double r19046 = r19032 * r19045;
        double r19047 = r19030 + r19046;
        double r19048 = 5.5;
        double r19049 = 8.0;
        double r19050 = pow(r19027, r19049);
        double r19051 = r19048 * r19050;
        double r19052 = r19047 + r19051;
        double r19053 = r19044 * r19027;
        double r19054 = r19031 / r19053;
        double r19055 = r19052 + r19054;
        return r19055;
}
↓
double f(double x, double y) {
        double r19056 = -2.0;
        double r19057 = x;
        double r19058 = 2.0;
        double r19059 = pow(r19057, r19058);
        double r19060 = r19056 * r19059;
        double r19061 = 2.0;
        double r19062 = y;
        double r19063 = r19061 * r19062;
        double r19064 = r19057 / r19063;
        double r19065 = r19060 + r19064;
        return r19065;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]

  2. Taylor expanded around 0 57.1

    \[\leadsto \color{blue}{-2 \cdot {x}^{2}} + \frac{x}{2 \cdot y}\]

  3. Final simplification57.1

    \[\leadsto -2 \cdot {x}^{2} + \frac{x}{2 \cdot y}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Rump's expression from Stadtherr's award speech"
  :precision binary64
  :pre (and (== x 77617) (== y 33096))
  (+ (+ (+ (* 333.75 (pow y 6)) (* (* x x) (- (- (- (* (* (* (* 11 x) x) y) y) (pow y 6)) (* 121 (pow y 4))) 2))) (* 5.5 (pow y 8))) (/ x (* 2 y))))