Average Error: 58.1 → 57.1
Time: 11.4s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[\frac{0.5}{\frac{y}{x}} - 2 \cdot \left(x \cdot x\right)\]
\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{0.5}{\frac{y}{x}} - 2 \cdot \left(x \cdot x\right)
double f(double x, double y) {
        double r22105 = 333.75;
        double r22106 = y;
        double r22107 = 6.0;
        double r22108 = pow(r22106, r22107);
        double r22109 = r22105 * r22108;
        double r22110 = x;
        double r22111 = r22110 * r22110;
        double r22112 = 11.0;
        double r22113 = r22112 * r22110;
        double r22114 = r22113 * r22110;
        double r22115 = r22114 * r22106;
        double r22116 = r22115 * r22106;
        double r22117 = r22116 - r22108;
        double r22118 = 121.0;
        double r22119 = 4.0;
        double r22120 = pow(r22106, r22119);
        double r22121 = r22118 * r22120;
        double r22122 = r22117 - r22121;
        double r22123 = 2.0;
        double r22124 = r22122 - r22123;
        double r22125 = r22111 * r22124;
        double r22126 = r22109 + r22125;
        double r22127 = 5.5;
        double r22128 = 8.0;
        double r22129 = pow(r22106, r22128);
        double r22130 = r22127 * r22129;
        double r22131 = r22126 + r22130;
        double r22132 = r22123 * r22106;
        double r22133 = r22110 / r22132;
        double r22134 = r22131 + r22133;
        return r22134;
}
↓
double f(double x, double y) {
        double r22135 = 0.5;
        double r22136 = y;
        double r22137 = x;
        double r22138 = r22136 / r22137;
        double r22139 = r22135 / r22138;
        double r22140 = 2.0;
        double r22141 = r22137 * r22137;
        double r22142 = r22140 * r22141;
        double r22143 = r22139 - r22142;
        return r22143;
}

Error

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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. Simplified58.1

    \[\leadsto \color{blue}{\left(\left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(11 \cdot \left(x \cdot x\right)\right)\right) \cdot y - {y}^{6}\right) - \left(2 + {y}^{4} \cdot 121\right)\right) + {y}^{6} \cdot 333.75\right) + \left({y}^{8} \cdot 5.5 + \frac{x}{2 \cdot y}\right)}\]

  3. Taylor expanded around 0 57.1

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

  4. Simplified57.1

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

  5. Final simplification57.1

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

Reproduce

herbie shell --seed 2019195 
(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))))