Average Error: 58.1 → 57.1
Time: 13.5s
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 r19308 = 333.75;
        double r19309 = y;
        double r19310 = 6.0;
        double r19311 = pow(r19309, r19310);
        double r19312 = r19308 * r19311;
        double r19313 = x;
        double r19314 = r19313 * r19313;
        double r19315 = 11.0;
        double r19316 = r19315 * r19313;
        double r19317 = r19316 * r19313;
        double r19318 = r19317 * r19309;
        double r19319 = r19318 * r19309;
        double r19320 = r19319 - r19311;
        double r19321 = 121.0;
        double r19322 = 4.0;
        double r19323 = pow(r19309, r19322);
        double r19324 = r19321 * r19323;
        double r19325 = r19320 - r19324;
        double r19326 = 2.0;
        double r19327 = r19325 - r19326;
        double r19328 = r19314 * r19327;
        double r19329 = r19312 + r19328;
        double r19330 = 5.5;
        double r19331 = 8.0;
        double r19332 = pow(r19309, r19331);
        double r19333 = r19330 * r19332;
        double r19334 = r19329 + r19333;
        double r19335 = r19326 * r19309;
        double r19336 = r19313 / r19335;
        double r19337 = r19334 + r19336;
        return r19337;
}
↓
double f(double x, double y) {
        double r19338 = -2.0;
        double r19339 = x;
        double r19340 = 2.0;
        double r19341 = pow(r19339, r19340);
        double r19342 = r19338 * r19341;
        double r19343 = 2.0;
        double r19344 = y;
        double r19345 = r19343 * r19344;
        double r19346 = r19339 / r19345;
        double r19347 = r19342 + r19346;
        return r19347;
}

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 2019347 
(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))))