Average Error: 58.1 → 58.1
Time: 14.4s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617 \cdot 77617, \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right) + \mathsf{fma}\left({33096}^{4}, -121, -2\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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, \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right) + \mathsf{fma}\left({33096}^{4}, -121, -2\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)
double f() {
        double r71253 = 333.75;
        double r71254 = 33096.0;
        double r71255 = 6.0;
        double r71256 = pow(r71254, r71255);
        double r71257 = r71253 * r71256;
        double r71258 = 77617.0;
        double r71259 = r71258 * r71258;
        double r71260 = 11.0;
        double r71261 = r71260 * r71259;
        double r71262 = r71254 * r71254;
        double r71263 = r71261 * r71262;
        double r71264 = -r71256;
        double r71265 = r71263 + r71264;
        double r71266 = -121.0;
        double r71267 = 4.0;
        double r71268 = pow(r71254, r71267);
        double r71269 = r71266 * r71268;
        double r71270 = r71265 + r71269;
        double r71271 = -2.0;
        double r71272 = r71270 + r71271;
        double r71273 = r71259 * r71272;
        double r71274 = r71257 + r71273;
        double r71275 = 5.5;
        double r71276 = 8.0;
        double r71277 = pow(r71254, r71276);
        double r71278 = r71275 * r71277;
        double r71279 = r71274 + r71278;
        double r71280 = 2.0;
        double r71281 = r71280 * r71254;
        double r71282 = r71258 / r71281;
        double r71283 = r71279 + r71282;
        return r71283;
}
↓
double f() {
        double r71284 = 77617.0;
        double r71285 = r71284 * r71284;
        double r71286 = 11.0;
        double r71287 = r71286 * r71285;
        double r71288 = 33096.0;
        double r71289 = r71288 * r71288;
        double r71290 = r71287 * r71289;
        double r71291 = 6.0;
        double r71292 = pow(r71288, r71291);
        double r71293 = r71290 - r71292;
        double r71294 = 4.0;
        double r71295 = pow(r71288, r71294);
        double r71296 = -121.0;
        double r71297 = -2.0;
        double r71298 = fma(r71295, r71296, r71297);
        double r71299 = r71293 + r71298;
        double r71300 = 333.75;
        double r71301 = 5.5;
        double r71302 = 8.0;
        double r71303 = pow(r71288, r71302);
        double r71304 = 2.0;
        double r71305 = r71304 * r71288;
        double r71306 = r71284 / r71305;
        double r71307 = fma(r71301, r71303, r71306);
        double r71308 = fma(r71292, r71300, r71307);
        double r71309 = fma(r71285, r71299, r71308);
        return r71309;
}

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

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

  3. Final simplification58.1

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096))))