Average Error: 58.1 → 58.1
Time: 2.7s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]
\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}
↓
\sqrt[3]{{\left(\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)\right)}^{3}}
double f() {
        double r62003 = 333.75;
        double r62004 = 33096.0;
        double r62005 = 6.0;
        double r62006 = pow(r62004, r62005);
        double r62007 = r62003 * r62006;
        double r62008 = 77617.0;
        double r62009 = r62008 * r62008;
        double r62010 = 11.0;
        double r62011 = r62010 * r62009;
        double r62012 = r62004 * r62004;
        double r62013 = r62011 * r62012;
        double r62014 = -r62006;
        double r62015 = r62013 + r62014;
        double r62016 = -121.0;
        double r62017 = 4.0;
        double r62018 = pow(r62004, r62017);
        double r62019 = r62016 * r62018;
        double r62020 = r62015 + r62019;
        double r62021 = -2.0;
        double r62022 = r62020 + r62021;
        double r62023 = r62009 * r62022;
        double r62024 = r62007 + r62023;
        double r62025 = 5.5;
        double r62026 = 8.0;
        double r62027 = pow(r62004, r62026);
        double r62028 = r62025 * r62027;
        double r62029 = r62024 + r62028;
        double r62030 = 2.0;
        double r62031 = r62030 * r62004;
        double r62032 = r62008 / r62031;
        double r62033 = r62029 + r62032;
        return r62033;
}
↓
double f() {
        double r62034 = 77617.0;
        double r62035 = 11.0;
        double r62036 = r62034 * r62034;
        double r62037 = r62035 * r62036;
        double r62038 = 33096.0;
        double r62039 = r62038 * r62038;
        double r62040 = r62037 * r62039;
        double r62041 = 6.0;
        double r62042 = pow(r62038, r62041);
        double r62043 = 4.0;
        double r62044 = pow(r62038, r62043);
        double r62045 = -121.0;
        double r62046 = -2.0;
        double r62047 = fma(r62044, r62045, r62046);
        double r62048 = r62042 - r62047;
        double r62049 = r62040 - r62048;
        double r62050 = r62034 * r62049;
        double r62051 = 333.75;
        double r62052 = 8.0;
        double r62053 = pow(r62038, r62052);
        double r62054 = 5.5;
        double r62055 = 2.0;
        double r62056 = r62055 * r62038;
        double r62057 = r62034 / r62056;
        double r62058 = fma(r62053, r62054, r62057);
        double r62059 = fma(r62051, r62042, r62058);
        double r62060 = fma(r62034, r62050, r62059);
        double r62061 = 3.0;
        double r62062 = pow(r62060, r62061);
        double r62063 = cbrt(r62062);
        return r62063;
}

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. Using strategy rm

  4. Applied add-cbrt-cube58.1

    \[\leadsto \color{blue}{\sqrt[3]{\left(\mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right) \cdot \mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right) \cdot \mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)}}\]

  5. Simplified58.1

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}}\]

  6. Final simplification58.1

    \[\leadsto \sqrt[3]{{\left(\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]

Reproduce

herbie shell --seed 2019354 +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))))