Average Error: 58.1 → 58.1
Time: 2.5s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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 r53156 = 333.75;
        double r53157 = 33096.0;
        double r53158 = 6.0;
        double r53159 = pow(r53157, r53158);
        double r53160 = r53156 * r53159;
        double r53161 = 77617.0;
        double r53162 = r53161 * r53161;
        double r53163 = 11.0;
        double r53164 = r53163 * r53162;
        double r53165 = r53157 * r53157;
        double r53166 = r53164 * r53165;
        double r53167 = -r53159;
        double r53168 = r53166 + r53167;
        double r53169 = -121.0;
        double r53170 = 4.0;
        double r53171 = pow(r53157, r53170);
        double r53172 = r53169 * r53171;
        double r53173 = r53168 + r53172;
        double r53174 = -2.0;
        double r53175 = r53173 + r53174;
        double r53176 = r53162 * r53175;
        double r53177 = r53160 + r53176;
        double r53178 = 5.5;
        double r53179 = 8.0;
        double r53180 = pow(r53157, r53179);
        double r53181 = r53178 * r53180;
        double r53182 = r53177 + r53181;
        double r53183 = 2.0;
        double r53184 = r53183 * r53157;
        double r53185 = r53161 / r53184;
        double r53186 = r53182 + r53185;
        return r53186;
}
↓
double f() {
        double r53187 = 77617.0;
        double r53188 = 11.0;
        double r53189 = r53187 * r53187;
        double r53190 = r53188 * r53189;
        double r53191 = 33096.0;
        double r53192 = r53191 * r53191;
        double r53193 = r53190 * r53192;
        double r53194 = 6.0;
        double r53195 = pow(r53191, r53194);
        double r53196 = 4.0;
        double r53197 = pow(r53191, r53196);
        double r53198 = -121.0;
        double r53199 = -2.0;
        double r53200 = fma(r53197, r53198, r53199);
        double r53201 = r53195 - r53200;
        double r53202 = r53193 - r53201;
        double r53203 = r53187 * r53202;
        double r53204 = 333.75;
        double r53205 = 8.0;
        double r53206 = pow(r53191, r53205);
        double r53207 = 5.5;
        double r53208 = 2.0;
        double r53209 = r53208 * r53191;
        double r53210 = r53187 / r53209;
        double r53211 = fma(r53206, r53207, r53210);
        double r53212 = fma(r53204, r53195, r53211);
        double r53213 = fma(r53187, r53203, r53212);
        return r53213;
}

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 2020018 +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))))