Average Error: 58.1 → 57.1
Time: 10.7s
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 r19116 = 333.75;
        double r19117 = y;
        double r19118 = 6.0;
        double r19119 = pow(r19117, r19118);
        double r19120 = r19116 * r19119;
        double r19121 = x;
        double r19122 = r19121 * r19121;
        double r19123 = 11.0;
        double r19124 = r19123 * r19121;
        double r19125 = r19124 * r19121;
        double r19126 = r19125 * r19117;
        double r19127 = r19126 * r19117;
        double r19128 = r19127 - r19119;
        double r19129 = 121.0;
        double r19130 = 4.0;
        double r19131 = pow(r19117, r19130);
        double r19132 = r19129 * r19131;
        double r19133 = r19128 - r19132;
        double r19134 = 2.0;
        double r19135 = r19133 - r19134;
        double r19136 = r19122 * r19135;
        double r19137 = r19120 + r19136;
        double r19138 = 5.5;
        double r19139 = 8.0;
        double r19140 = pow(r19117, r19139);
        double r19141 = r19138 * r19140;
        double r19142 = r19137 + r19141;
        double r19143 = r19134 * r19117;
        double r19144 = r19121 / r19143;
        double r19145 = r19142 + r19144;
        return r19145;
}
↓
double f(double x, double y) {
        double r19146 = -2.0;
        double r19147 = x;
        double r19148 = 2.0;
        double r19149 = pow(r19147, r19148);
        double r19150 = r19146 * r19149;
        double r19151 = 2.0;
        double r19152 = y;
        double r19153 = r19151 * r19152;
        double r19154 = r19147 / r19153;
        double r19155 = r19150 + r19154;
        return r19155;
}

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 2019235 
(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))))