Average Error: 58.1 → 58.1
Time: 2.6s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)
double f() {
        double r58178 = 333.75;
        double r58179 = 33096.0;
        double r58180 = 6.0;
        double r58181 = pow(r58179, r58180);
        double r58182 = r58178 * r58181;
        double r58183 = 77617.0;
        double r58184 = r58183 * r58183;
        double r58185 = 11.0;
        double r58186 = r58185 * r58184;
        double r58187 = r58179 * r58179;
        double r58188 = r58186 * r58187;
        double r58189 = -r58181;
        double r58190 = r58188 + r58189;
        double r58191 = -121.0;
        double r58192 = 4.0;
        double r58193 = pow(r58179, r58192);
        double r58194 = r58191 * r58193;
        double r58195 = r58190 + r58194;
        double r58196 = -2.0;
        double r58197 = r58195 + r58196;
        double r58198 = r58184 * r58197;
        double r58199 = r58182 + r58198;
        double r58200 = 5.5;
        double r58201 = 8.0;
        double r58202 = pow(r58179, r58201);
        double r58203 = r58200 * r58202;
        double r58204 = r58199 + r58203;
        double r58205 = 2.0;
        double r58206 = r58205 * r58179;
        double r58207 = r58183 / r58206;
        double r58208 = r58204 + r58207;
        return r58208;
}
↓
double f() {
        double r58209 = 77617.0;
        double r58210 = 11.0;
        double r58211 = r58209 * r58209;
        double r58212 = r58210 * r58211;
        double r58213 = 33096.0;
        double r58214 = r58213 * r58213;
        double r58215 = r58212 * r58214;
        double r58216 = 6.0;
        double r58217 = pow(r58213, r58216);
        double r58218 = 4.0;
        double r58219 = pow(r58213, r58218);
        double r58220 = -121.0;
        double r58221 = -2.0;
        double r58222 = fma(r58219, r58220, r58221);
        double r58223 = r58217 - r58222;
        double r58224 = r58215 - r58223;
        double r58225 = r58209 * r58224;
        double r58226 = 333.75;
        double r58227 = 8.0;
        double r58228 = pow(r58213, r58227);
        double r58229 = 5.5;
        double r58230 = 2.0;
        double r58231 = r58230 * r58213;
        double r58232 = r58209 / r58231;
        double r58233 = fma(r58228, r58229, r58232);
        double r58234 = fma(r58226, r58217, r58233);
        double r58235 = fma(r58209, r58225, r58234);
        return r58235;
}

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

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

  3. Simplified58.1

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

  4. Final simplification58.1

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

Reproduce

herbie shell --seed 2020002 +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))))