Average Error: 0.5 → 0.7
Time: 59.1s
Precision: 64
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
↓
\[\left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3} \cdot \left(\sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3} \cdot \sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 4 - 6\right)\right)\right)\right)\right) + \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 3\right) + x1\]
x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)
↓
\left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3} \cdot \left(\sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3} \cdot \sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 4 - 6\right)\right)\right)\right)\right) + \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 3\right) + x1
double f(double x1, double x2) {
        double r3402834 = x1;
        double r3402835 = 2.0;
        double r3402836 = r3402835 * r3402834;
        double r3402837 = 3.0;
        double r3402838 = r3402837 * r3402834;
        double r3402839 = r3402838 * r3402834;
        double r3402840 = x2;
        double r3402841 = r3402835 * r3402840;
        double r3402842 = r3402839 + r3402841;
        double r3402843 = r3402842 - r3402834;
        double r3402844 = r3402834 * r3402834;
        double r3402845 = 1.0;
        double r3402846 = r3402844 + r3402845;
        double r3402847 = r3402843 / r3402846;
        double r3402848 = r3402836 * r3402847;
        double r3402849 = r3402847 - r3402837;
        double r3402850 = r3402848 * r3402849;
        double r3402851 = 4.0;
        double r3402852 = r3402851 * r3402847;
        double r3402853 = 6.0;
        double r3402854 = r3402852 - r3402853;
        double r3402855 = r3402844 * r3402854;
        double r3402856 = r3402850 + r3402855;
        double r3402857 = r3402856 * r3402846;
        double r3402858 = r3402839 * r3402847;
        double r3402859 = r3402857 + r3402858;
        double r3402860 = r3402844 * r3402834;
        double r3402861 = r3402859 + r3402860;
        double r3402862 = r3402861 + r3402834;
        double r3402863 = r3402839 - r3402841;
        double r3402864 = r3402863 - r3402834;
        double r3402865 = r3402864 / r3402846;
        double r3402866 = r3402837 * r3402865;
        double r3402867 = r3402862 + r3402866;
        double r3402868 = r3402834 + r3402867;
        return r3402868;
}
↓
double f(double x1, double x2) {
        double r3402869 = x1;
        double r3402870 = r3402869 * r3402869;
        double r3402871 = r3402869 * r3402870;
        double r3402872 = 3.0;
        double r3402873 = r3402872 * r3402869;
        double r3402874 = r3402873 * r3402869;
        double r3402875 = x2;
        double r3402876 = 2.0;
        double r3402877 = r3402875 * r3402876;
        double r3402878 = r3402874 + r3402877;
        double r3402879 = r3402878 - r3402869;
        double r3402880 = 1.0;
        double r3402881 = r3402880 + r3402870;
        double r3402882 = r3402879 / r3402881;
        double r3402883 = r3402874 * r3402882;
        double r3402884 = r3402869 * r3402876;
        double r3402885 = r3402884 * r3402882;
        double r3402886 = r3402882 - r3402872;
        double r3402887 = cbrt(r3402886);
        double r3402888 = r3402887 * r3402887;
        double r3402889 = r3402887 * r3402888;
        double r3402890 = r3402885 * r3402889;
        double r3402891 = 4.0;
        double r3402892 = r3402882 * r3402891;
        double r3402893 = 6.0;
        double r3402894 = r3402892 - r3402893;
        double r3402895 = r3402870 * r3402894;
        double r3402896 = r3402890 + r3402895;
        double r3402897 = r3402881 * r3402896;
        double r3402898 = r3402883 + r3402897;
        double r3402899 = r3402871 + r3402898;
        double r3402900 = r3402869 + r3402899;
        double r3402901 = r3402874 - r3402877;
        double r3402902 = r3402901 - r3402869;
        double r3402903 = r3402902 / r3402881;
        double r3402904 = r3402903 * r3402872;
        double r3402905 = r3402900 + r3402904;
        double r3402906 = r3402905 + r3402869;
        return r3402906;
}

Error

Bits error versus x1

Bits error versus x2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.7

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3} \cdot \sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3}\right) \cdot \sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3}\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

  4. Final simplification0.7

    \[\leadsto \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(\sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3} \cdot \left(\sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3} \cdot \sqrt[3]{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} - 3}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 4 - 6\right)\right)\right)\right)\right) + \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 3\right) + x1\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (+ (* x1 x1) 1.0)) (* (* (* 3.0 x1) x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (* (* x1 x1) x1)) x1) (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))