Average Error: 58.1 → 57.1
Time: 5.4s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}\]
\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}
↓
0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}
double f(double x, double y) {
        double r11254 = 333.75;
        double r11255 = y;
        double r11256 = 6.0;
        double r11257 = pow(r11255, r11256);
        double r11258 = r11254 * r11257;
        double r11259 = x;
        double r11260 = r11259 * r11259;
        double r11261 = 11.0;
        double r11262 = r11261 * r11259;
        double r11263 = r11262 * r11259;
        double r11264 = r11263 * r11255;
        double r11265 = r11264 * r11255;
        double r11266 = r11265 - r11257;
        double r11267 = 121.0;
        double r11268 = 4.0;
        double r11269 = pow(r11255, r11268);
        double r11270 = r11267 * r11269;
        double r11271 = r11266 - r11270;
        double r11272 = 2.0;
        double r11273 = r11271 - r11272;
        double r11274 = r11260 * r11273;
        double r11275 = r11258 + r11274;
        double r11276 = 5.5;
        double r11277 = 8.0;
        double r11278 = pow(r11255, r11277);
        double r11279 = r11276 * r11278;
        double r11280 = r11275 + r11279;
        double r11281 = r11272 * r11255;
        double r11282 = r11259 / r11281;
        double r11283 = r11280 + r11282;
        return r11283;
}
↓
double f(double x, double y) {
        double r11284 = 0.5;
        double r11285 = x;
        double r11286 = y;
        double r11287 = r11285 / r11286;
        double r11288 = r11284 * r11287;
        double r11289 = 2.0;
        double r11290 = 2.0;
        double r11291 = pow(r11285, r11290);
        double r11292 = r11289 * r11291;
        double r11293 = r11288 - r11292;
        return r11293;
}

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

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

  3. Taylor expanded around 0 57.1

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

  4. Final simplification57.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(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))))