Average Error: 0.1 → 0.1
Time: 51.2s
Precision: 64
\[\left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\left(11 \cdot {a}^{2}\right) \cdot {b}^{2} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}\]
\[\left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\left({b}^{\left(\frac{2}{2}\right)} \cdot \left(11 \cdot {a}^{2}\right)\right) \cdot {b}^{\left(\frac{2}{2}\right)} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}\]
\left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\left(11 \cdot {a}^{2}\right) \cdot {b}^{2} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}
\left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\left({b}^{\left(\frac{2}{2}\right)} \cdot \left(11 \cdot {a}^{2}\right)\right) \cdot {b}^{\left(\frac{2}{2}\right)} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}
double f(double a, double b) {
        double r140863 = 333.75;
        double r140864 = b;
        double r140865 = 6.0;
        double r140866 = pow(r140864, r140865);
        double r140867 = r140863 * r140866;
        double r140868 = a;
        double r140869 = 2.0;
        double r140870 = pow(r140868, r140869);
        double r140871 = 11.0;
        double r140872 = r140871 * r140870;
        double r140873 = pow(r140864, r140869);
        double r140874 = r140872 * r140873;
        double r140875 = r140874 - r140866;
        double r140876 = 121.0;
        double r140877 = 4.0;
        double r140878 = pow(r140864, r140877);
        double r140879 = r140876 * r140878;
        double r140880 = r140875 - r140879;
        double r140881 = r140880 - r140869;
        double r140882 = r140870 * r140881;
        double r140883 = r140867 + r140882;
        double r140884 = 5.5;
        double r140885 = 8.0;
        double r140886 = pow(r140864, r140885);
        double r140887 = r140884 * r140886;
        double r140888 = r140883 + r140887;
        double r140889 = r140869 * r140864;
        double r140890 = r140868 / r140889;
        double r140891 = r140888 + r140890;
        return r140891;
}

double f(double a, double b) {
        double r140892 = 333.75;
        double r140893 = b;
        double r140894 = 6.0;
        double r140895 = pow(r140893, r140894);
        double r140896 = r140892 * r140895;
        double r140897 = a;
        double r140898 = 2.0;
        double r140899 = pow(r140897, r140898);
        double r140900 = 2.0;
        double r140901 = r140898 / r140900;
        double r140902 = pow(r140893, r140901);
        double r140903 = 11.0;
        double r140904 = r140903 * r140899;
        double r140905 = r140902 * r140904;
        double r140906 = r140905 * r140902;
        double r140907 = r140906 - r140895;
        double r140908 = 121.0;
        double r140909 = 4.0;
        double r140910 = pow(r140893, r140909);
        double r140911 = r140908 * r140910;
        double r140912 = r140907 - r140911;
        double r140913 = r140912 - r140898;
        double r140914 = r140899 * r140913;
        double r140915 = r140896 + r140914;
        double r140916 = 5.5;
        double r140917 = 8.0;
        double r140918 = pow(r140893, r140917);
        double r140919 = r140916 * r140918;
        double r140920 = r140915 + r140919;
        double r140921 = r140898 * r140893;
        double r140922 = r140897 / r140921;
        double r140923 = r140920 + r140922;
        return r140923;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\left(11 \cdot {a}^{2}\right) \cdot {b}^{2} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}\]
  2. Using strategy rm
  3. Applied sqr-pow0.1

    \[\leadsto \left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\left(11 \cdot {a}^{2}\right) \cdot \color{blue}{\left({b}^{\left(\frac{2}{2}\right)} \cdot {b}^{\left(\frac{2}{2}\right)}\right)} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}\]
  4. Applied associate-*r*0.1

    \[\leadsto \left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\color{blue}{\left(\left(11 \cdot {a}^{2}\right) \cdot {b}^{\left(\frac{2}{2}\right)}\right) \cdot {b}^{\left(\frac{2}{2}\right)}} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}\]
  5. Simplified0.1

    \[\leadsto \left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\color{blue}{\left({b}^{\left(\frac{2}{2}\right)} \cdot \left(11 \cdot {a}^{2}\right)\right)} \cdot {b}^{\left(\frac{2}{2}\right)} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}\]
  6. Final simplification0.1

    \[\leadsto \left(\left(333.75 \cdot {b}^{6} + {a}^{2} \cdot \left(\left(\left(\left({b}^{\left(\frac{2}{2}\right)} \cdot \left(11 \cdot {a}^{2}\right)\right) \cdot {b}^{\left(\frac{2}{2}\right)} - {b}^{6}\right) - 121 \cdot {b}^{4}\right) - 2\right)\right) + 5.5 \cdot {b}^{8}\right) + \frac{a}{2 \cdot b}\]

Reproduce

herbie shell --seed 1 
(FPCore (a b)
  :name "Rump's example, with pow"
  (+ (+ (+ (* 333.75 (pow b 6.0)) (* (pow a 2.0) (- (- (- (* (* 11.0 (pow a 2.0)) (pow b 2.0)) (pow b 6.0)) (* 121.0 (pow b 4.0))) 2.0))) (* 5.5 (pow b 8.0))) (/ a (* 2.0 b))))