Average Error: 58.1 → 57.1
Time: 18.1s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[\frac{x \cdot 0.5}{y} - x \cdot \left(2 \cdot x\right)\]
\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}
↓
\frac{x \cdot 0.5}{y} - x \cdot \left(2 \cdot x\right)
double f(double x, double y) {
        double r17098 = 333.75;
        double r17099 = y;
        double r17100 = 6.0;
        double r17101 = pow(r17099, r17100);
        double r17102 = r17098 * r17101;
        double r17103 = x;
        double r17104 = r17103 * r17103;
        double r17105 = 11.0;
        double r17106 = r17105 * r17103;
        double r17107 = r17106 * r17103;
        double r17108 = r17107 * r17099;
        double r17109 = r17108 * r17099;
        double r17110 = r17109 - r17101;
        double r17111 = 121.0;
        double r17112 = 4.0;
        double r17113 = pow(r17099, r17112);
        double r17114 = r17111 * r17113;
        double r17115 = r17110 - r17114;
        double r17116 = 2.0;
        double r17117 = r17115 - r17116;
        double r17118 = r17104 * r17117;
        double r17119 = r17102 + r17118;
        double r17120 = 5.5;
        double r17121 = 8.0;
        double r17122 = pow(r17099, r17121);
        double r17123 = r17120 * r17122;
        double r17124 = r17119 + r17123;
        double r17125 = r17116 * r17099;
        double r17126 = r17103 / r17125;
        double r17127 = r17124 + r17126;
        return r17127;
}
↓
double f(double x, double y) {
        double r17128 = x;
        double r17129 = 0.5;
        double r17130 = r17128 * r17129;
        double r17131 = y;
        double r17132 = r17130 / r17131;
        double r17133 = 2.0;
        double r17134 = r17133 * r17128;
        double r17135 = r17128 * r17134;
        double r17136 = r17132 - r17135;
        return r17136;
}

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

    \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}}\]

  3. Simplified57.1

    \[\leadsto \color{blue}{\frac{x \cdot 0.5}{y} - \left(2 \cdot x\right) \cdot x}\]

  4. Final simplification57.1

    \[\leadsto \frac{x \cdot 0.5}{y} - x \cdot \left(2 \cdot x\right)\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Rump's expression from Stadtherr's award speech"
  :pre (and (== x 77617.0) (== y 33096.0))
  (+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y))))