Average Error: 58.1 → 57.1
Time: 14.0s
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 r19093 = 333.75;
        double r19094 = y;
        double r19095 = 6.0;
        double r19096 = pow(r19094, r19095);
        double r19097 = r19093 * r19096;
        double r19098 = x;
        double r19099 = r19098 * r19098;
        double r19100 = 11.0;
        double r19101 = r19100 * r19098;
        double r19102 = r19101 * r19098;
        double r19103 = r19102 * r19094;
        double r19104 = r19103 * r19094;
        double r19105 = r19104 - r19096;
        double r19106 = 121.0;
        double r19107 = 4.0;
        double r19108 = pow(r19094, r19107);
        double r19109 = r19106 * r19108;
        double r19110 = r19105 - r19109;
        double r19111 = 2.0;
        double r19112 = r19110 - r19111;
        double r19113 = r19099 * r19112;
        double r19114 = r19097 + r19113;
        double r19115 = 5.5;
        double r19116 = 8.0;
        double r19117 = pow(r19094, r19116);
        double r19118 = r19115 * r19117;
        double r19119 = r19114 + r19118;
        double r19120 = r19111 * r19094;
        double r19121 = r19098 / r19120;
        double r19122 = r19119 + r19121;
        return r19122;
}
↓
double f(double x, double y) {
        double r19123 = -2.0;
        double r19124 = x;
        double r19125 = 2.0;
        double r19126 = pow(r19124, r19125);
        double r19127 = r19123 * r19126;
        double r19128 = 2.0;
        double r19129 = y;
        double r19130 = r19128 * r19129;
        double r19131 = r19124 / r19130;
        double r19132 = r19127 + r19131;
        return r19132;
}

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 2019325 
(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))))