Average Error: 58.1 → 57.1
Time: 14.7s
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 r19117 = 333.75;
        double r19118 = y;
        double r19119 = 6.0;
        double r19120 = pow(r19118, r19119);
        double r19121 = r19117 * r19120;
        double r19122 = x;
        double r19123 = r19122 * r19122;
        double r19124 = 11.0;
        double r19125 = r19124 * r19122;
        double r19126 = r19125 * r19122;
        double r19127 = r19126 * r19118;
        double r19128 = r19127 * r19118;
        double r19129 = r19128 - r19120;
        double r19130 = 121.0;
        double r19131 = 4.0;
        double r19132 = pow(r19118, r19131);
        double r19133 = r19130 * r19132;
        double r19134 = r19129 - r19133;
        double r19135 = 2.0;
        double r19136 = r19134 - r19135;
        double r19137 = r19123 * r19136;
        double r19138 = r19121 + r19137;
        double r19139 = 5.5;
        double r19140 = 8.0;
        double r19141 = pow(r19118, r19140);
        double r19142 = r19139 * r19141;
        double r19143 = r19138 + r19142;
        double r19144 = r19135 * r19118;
        double r19145 = r19122 / r19144;
        double r19146 = r19143 + r19145;
        return r19146;
}
↓
double f(double x, double y) {
        double r19147 = -2.0;
        double r19148 = x;
        double r19149 = 2.0;
        double r19150 = pow(r19148, r19149);
        double r19151 = r19147 * r19150;
        double r19152 = 2.0;
        double r19153 = y;
        double r19154 = r19152 * r19153;
        double r19155 = r19148 / r19154;
        double r19156 = r19151 + r19155;
        return r19156;
}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019199 
(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))))