Average Error: 58.1 → 57.1
Time: 8.8s
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 r11100 = 333.75;
        double r11101 = y;
        double r11102 = 6.0;
        double r11103 = pow(r11101, r11102);
        double r11104 = r11100 * r11103;
        double r11105 = x;
        double r11106 = r11105 * r11105;
        double r11107 = 11.0;
        double r11108 = r11107 * r11105;
        double r11109 = r11108 * r11105;
        double r11110 = r11109 * r11101;
        double r11111 = r11110 * r11101;
        double r11112 = r11111 - r11103;
        double r11113 = 121.0;
        double r11114 = 4.0;
        double r11115 = pow(r11101, r11114);
        double r11116 = r11113 * r11115;
        double r11117 = r11112 - r11116;
        double r11118 = 2.0;
        double r11119 = r11117 - r11118;
        double r11120 = r11106 * r11119;
        double r11121 = r11104 + r11120;
        double r11122 = 5.5;
        double r11123 = 8.0;
        double r11124 = pow(r11101, r11123);
        double r11125 = r11122 * r11124;
        double r11126 = r11121 + r11125;
        double r11127 = r11118 * r11101;
        double r11128 = r11105 / r11127;
        double r11129 = r11126 + r11128;
        return r11129;
}
↓
double f(double x, double y) {
        double r11130 = -2.0;
        double r11131 = x;
        double r11132 = 2.0;
        double r11133 = pow(r11131, r11132);
        double r11134 = r11130 * r11133;
        double r11135 = 2.0;
        double r11136 = y;
        double r11137 = r11135 * r11136;
        double r11138 = r11131 / r11137;
        double r11139 = r11134 + r11138;
        return r11139;
}

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 2019350 
(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))))