Average Error: 58.1 → 57.1
Time: 14.4s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[-2 \cdot {x}^{2} + \frac{x}{2 \cdot y}\]
\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 r19062 = 333.75;
        double r19063 = y;
        double r19064 = 6.0;
        double r19065 = pow(r19063, r19064);
        double r19066 = r19062 * r19065;
        double r19067 = x;
        double r19068 = r19067 * r19067;
        double r19069 = 11.0;
        double r19070 = r19069 * r19067;
        double r19071 = r19070 * r19067;
        double r19072 = r19071 * r19063;
        double r19073 = r19072 * r19063;
        double r19074 = r19073 - r19065;
        double r19075 = 121.0;
        double r19076 = 4.0;
        double r19077 = pow(r19063, r19076);
        double r19078 = r19075 * r19077;
        double r19079 = r19074 - r19078;
        double r19080 = 2.0;
        double r19081 = r19079 - r19080;
        double r19082 = r19068 * r19081;
        double r19083 = r19066 + r19082;
        double r19084 = 5.5;
        double r19085 = 8.0;
        double r19086 = pow(r19063, r19085);
        double r19087 = r19084 * r19086;
        double r19088 = r19083 + r19087;
        double r19089 = r19080 * r19063;
        double r19090 = r19067 / r19089;
        double r19091 = r19088 + r19090;
        return r19091;
}
↓
double f(double x, double y) {
        double r19092 = -2.0;
        double r19093 = x;
        double r19094 = 2.0;
        double r19095 = pow(r19093, r19094);
        double r19096 = r19092 * r19095;
        double r19097 = 2.0;
        double r19098 = y;
        double r19099 = r19097 * r19098;
        double r19100 = r19093 / r19099;
        double r19101 = r19096 + r19100;
        return r19101;
}

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))))