Average Error: 58.1 → 58.1
Time: 16.5s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617 \cdot \left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right) + \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 77617, \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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 \left(\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)\right), 77617, \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)
double f() {
        double r30218 = 333.75;
        double r30219 = 33096.0;
        double r30220 = 6.0;
        double r30221 = pow(r30219, r30220);
        double r30222 = r30218 * r30221;
        double r30223 = 77617.0;
        double r30224 = r30223 * r30223;
        double r30225 = 11.0;
        double r30226 = r30225 * r30224;
        double r30227 = r30219 * r30219;
        double r30228 = r30226 * r30227;
        double r30229 = -r30221;
        double r30230 = r30228 + r30229;
        double r30231 = -121.0;
        double r30232 = 4.0;
        double r30233 = pow(r30219, r30232);
        double r30234 = r30231 * r30233;
        double r30235 = r30230 + r30234;
        double r30236 = -2.0;
        double r30237 = r30235 + r30236;
        double r30238 = r30224 * r30237;
        double r30239 = r30222 + r30238;
        double r30240 = 5.5;
        double r30241 = 8.0;
        double r30242 = pow(r30219, r30241);
        double r30243 = r30240 * r30242;
        double r30244 = r30239 + r30243;
        double r30245 = 2.0;
        double r30246 = r30245 * r30219;
        double r30247 = r30223 / r30246;
        double r30248 = r30244 + r30247;
        return r30248;
}
↓
double f() {
        double r30249 = 77617.0;
        double r30250 = 11.0;
        double r30251 = r30249 * r30249;
        double r30252 = r30250 * r30251;
        double r30253 = 33096.0;
        double r30254 = r30253 * r30253;
        double r30255 = r30252 * r30254;
        double r30256 = 6.0;
        double r30257 = pow(r30253, r30256);
        double r30258 = r30255 - r30257;
        double r30259 = 4.0;
        double r30260 = pow(r30253, r30259);
        double r30261 = -121.0;
        double r30262 = -2.0;
        double r30263 = fma(r30260, r30261, r30262);
        double r30264 = r30258 + r30263;
        double r30265 = r30249 * r30264;
        double r30266 = 333.75;
        double r30267 = 5.5;
        double r30268 = 8.0;
        double r30269 = pow(r30253, r30268);
        double r30270 = 2.0;
        double r30271 = r30270 * r30253;
        double r30272 = r30249 / r30271;
        double r30273 = fma(r30267, r30269, r30272);
        double r30274 = fma(r30266, r30257, r30273);
        double r30275 = fma(r30265, r30249, r30274);
        return r30275;
}

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. Using strategy rm

  3. Applied *-un-lft-identity58.1

    \[\leadsto \left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \color{blue}{1 \cdot \frac{77617}{2 \cdot 33096}}\]

  4. Applied *-un-lft-identity58.1

    \[\leadsto \color{blue}{1 \cdot \left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right)} + 1 \cdot \frac{77617}{2 \cdot 33096}\]

  5. Applied distribute-lft-out58.1

    \[\leadsto \color{blue}{1 \cdot \left(\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\right)}\]

  6. Simplified58.1

    \[\leadsto 1 \cdot \color{blue}{\mathsf{fma}\left(77617 \cdot 77617, \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right) + \mathsf{fma}\left({33096}^{4}, -121, -2\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)}\]

  7. Simplified58.1

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

  8. Final simplification58.1

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

Reproduce

herbie shell --seed 2019209 +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))))