Average Error: 58.1 → 58.1
Time: 10.5s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617 \cdot 77617, \mathsf{fma}\left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right), 11, \mathsf{fma}\left({33096}^{4}, -121, -2 - {33096}^{6}\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{\frac{77617}{33096}}{2}\right)\right)\right)\]
\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}
↓
\mathsf{fma}\left(77617 \cdot 77617, \mathsf{fma}\left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right), 11, \mathsf{fma}\left({33096}^{4}, -121, -2 - {33096}^{6}\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{\frac{77617}{33096}}{2}\right)\right)\right)
double f() {
        double r2838237 = 333.75;
        double r2838238 = 33096.0;
        double r2838239 = 6.0;
        double r2838240 = pow(r2838238, r2838239);
        double r2838241 = r2838237 * r2838240;
        double r2838242 = 77617.0;
        double r2838243 = r2838242 * r2838242;
        double r2838244 = 11.0;
        double r2838245 = r2838244 * r2838243;
        double r2838246 = r2838238 * r2838238;
        double r2838247 = r2838245 * r2838246;
        double r2838248 = -r2838240;
        double r2838249 = r2838247 + r2838248;
        double r2838250 = -121.0;
        double r2838251 = 4.0;
        double r2838252 = pow(r2838238, r2838251);
        double r2838253 = r2838250 * r2838252;
        double r2838254 = r2838249 + r2838253;
        double r2838255 = -2.0;
        double r2838256 = r2838254 + r2838255;
        double r2838257 = r2838243 * r2838256;
        double r2838258 = r2838241 + r2838257;
        double r2838259 = 5.5;
        double r2838260 = 8.0;
        double r2838261 = pow(r2838238, r2838260);
        double r2838262 = r2838259 * r2838261;
        double r2838263 = r2838258 + r2838262;
        double r2838264 = 2.0;
        double r2838265 = r2838264 * r2838238;
        double r2838266 = r2838242 / r2838265;
        double r2838267 = r2838263 + r2838266;
        return r2838267;
}
↓
double f() {
        double r2838268 = 77617.0;
        double r2838269 = r2838268 * r2838268;
        double r2838270 = 33096.0;
        double r2838271 = r2838268 * r2838270;
        double r2838272 = r2838271 * r2838271;
        double r2838273 = 11.0;
        double r2838274 = 4.0;
        double r2838275 = pow(r2838270, r2838274);
        double r2838276 = -121.0;
        double r2838277 = -2.0;
        double r2838278 = 6.0;
        double r2838279 = pow(r2838270, r2838278);
        double r2838280 = r2838277 - r2838279;
        double r2838281 = fma(r2838275, r2838276, r2838280);
        double r2838282 = fma(r2838272, r2838273, r2838281);
        double r2838283 = 333.75;
        double r2838284 = 8.0;
        double r2838285 = pow(r2838270, r2838284);
        double r2838286 = 5.5;
        double r2838287 = r2838268 / r2838270;
        double r2838288 = 2.0;
        double r2838289 = r2838287 / r2838288;
        double r2838290 = fma(r2838285, r2838286, r2838289);
        double r2838291 = fma(r2838283, r2838279, r2838290);
        double r2838292 = fma(r2838269, r2838282, r2838291);
        return r2838292;
}

Error

Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]

  2. Simplified58.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(77617 \cdot 77617, \mathsf{fma}\left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right), 11, \mathsf{fma}\left({33096}^{4}, -121, -2 - {33096}^{6}\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{\frac{77617}{33096}}{2}\right)\right)\right)}\]

  3. Final simplification58.1

    \[\leadsto \mathsf{fma}\left(77617 \cdot 77617, \mathsf{fma}\left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right), 11, \mathsf{fma}\left({33096}^{4}, -121, -2 - {33096}^{6}\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{\frac{77617}{33096}}{2}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0))))