Average Error: 58.1 → 57.1
Time: 12.2s
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 r19021 = 333.75;
        double r19022 = y;
        double r19023 = 6.0;
        double r19024 = pow(r19022, r19023);
        double r19025 = r19021 * r19024;
        double r19026 = x;
        double r19027 = r19026 * r19026;
        double r19028 = 11.0;
        double r19029 = r19028 * r19026;
        double r19030 = r19029 * r19026;
        double r19031 = r19030 * r19022;
        double r19032 = r19031 * r19022;
        double r19033 = r19032 - r19024;
        double r19034 = 121.0;
        double r19035 = 4.0;
        double r19036 = pow(r19022, r19035);
        double r19037 = r19034 * r19036;
        double r19038 = r19033 - r19037;
        double r19039 = 2.0;
        double r19040 = r19038 - r19039;
        double r19041 = r19027 * r19040;
        double r19042 = r19025 + r19041;
        double r19043 = 5.5;
        double r19044 = 8.0;
        double r19045 = pow(r19022, r19044);
        double r19046 = r19043 * r19045;
        double r19047 = r19042 + r19046;
        double r19048 = r19039 * r19022;
        double r19049 = r19026 / r19048;
        double r19050 = r19047 + r19049;
        return r19050;
}
↓
double f(double x, double y) {
        double r19051 = -2.0;
        double r19052 = x;
        double r19053 = 2.0;
        double r19054 = pow(r19052, r19053);
        double r19055 = r19051 * r19054;
        double r19056 = 2.0;
        double r19057 = y;
        double r19058 = r19056 * r19057;
        double r19059 = r19052 / r19058;
        double r19060 = r19055 + r19059;
        return r19060;
}

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 2019303 
(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))))