Average Error: 0.5 → 0.5
Time: 1.1m
Precision: 64
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
↓
\[\left(\left(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) + \left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(-3\right) + \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(x1 \cdot x1\right)\right) + \left(-6 \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(1 + x1 \cdot x1\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot 3\right) + x1\]
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(\left(\left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot \left(\left(2 \cdot x1\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) + \left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(-3\right) + \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \left(x1 \cdot x1\right)\right) + \left(-6 \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(1 + x1 \cdot x1\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{1 + x1 \cdot x1} \cdot 3\right) + x1
double f(double x1, double x2) {
        double r2530842 = x1;
        double r2530843 = 2.0;
        double r2530844 = r2530843 * r2530842;
        double r2530845 = 3.0;
        double r2530846 = r2530845 * r2530842;
        double r2530847 = r2530846 * r2530842;
        double r2530848 = x2;
        double r2530849 = r2530843 * r2530848;
        double r2530850 = r2530847 + r2530849;
        double r2530851 = r2530850 - r2530842;
        double r2530852 = r2530842 * r2530842;
        double r2530853 = 1.0;
        double r2530854 = r2530852 + r2530853;
        double r2530855 = r2530851 / r2530854;
        double r2530856 = r2530844 * r2530855;
        double r2530857 = r2530855 - r2530845;
        double r2530858 = r2530856 * r2530857;
        double r2530859 = 4.0;
        double r2530860 = r2530859 * r2530855;
        double r2530861 = 6.0;
        double r2530862 = r2530860 - r2530861;
        double r2530863 = r2530852 * r2530862;
        double r2530864 = r2530858 + r2530863;
        double r2530865 = r2530864 * r2530854;
        double r2530866 = r2530847 * r2530855;
        double r2530867 = r2530865 + r2530866;
        double r2530868 = r2530852 * r2530842;
        double r2530869 = r2530867 + r2530868;
        double r2530870 = r2530869 + r2530842;
        double r2530871 = r2530847 - r2530849;
        double r2530872 = r2530871 - r2530842;
        double r2530873 = r2530872 / r2530854;
        double r2530874 = r2530845 * r2530873;
        double r2530875 = r2530870 + r2530874;
        double r2530876 = r2530842 + r2530875;
        return r2530876;
}
↓
double f(double x1, double x2) {
        double r2530877 = x1;
        double r2530878 = 3.0;
        double r2530879 = r2530877 * r2530878;
        double r2530880 = r2530877 * r2530879;
        double r2530881 = 2.0;
        double r2530882 = x2;
        double r2530883 = r2530881 * r2530882;
        double r2530884 = r2530880 + r2530883;
        double r2530885 = r2530884 - r2530877;
        double r2530886 = 1.0;
        double r2530887 = r2530877 * r2530877;
        double r2530888 = r2530886 + r2530887;
        double r2530889 = r2530885 / r2530888;
        double r2530890 = r2530881 * r2530877;
        double r2530891 = r2530890 * r2530889;
        double r2530892 = r2530889 * r2530891;
        double r2530893 = -r2530878;
        double r2530894 = r2530891 * r2530893;
        double r2530895 = 4.0;
        double r2530896 = r2530895 * r2530889;
        double r2530897 = r2530896 * r2530887;
        double r2530898 = r2530894 + r2530897;
        double r2530899 = 6.0;
        double r2530900 = r2530899 * r2530887;
        double r2530901 = -r2530900;
        double r2530902 = r2530898 + r2530901;
        double r2530903 = r2530892 + r2530902;
        double r2530904 = r2530903 * r2530888;
        double r2530905 = r2530889 * r2530880;
        double r2530906 = r2530904 + r2530905;
        double r2530907 = r2530887 * r2530877;
        double r2530908 = r2530906 + r2530907;
        double r2530909 = r2530908 + r2530877;
        double r2530910 = r2530880 - r2530883;
        double r2530911 = r2530910 - r2530877;
        double r2530912 = r2530911 / r2530888;
        double r2530913 = r2530912 * r2530878;
        double r2530914 = r2530909 + r2530913;
        double r2530915 = r2530914 + r2530877;
        return r2530915;
}

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 sub-neg0.5

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

  4. Applied distribute-rgt-in0.5

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

  5. Applied associate-+l+0.5

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

  7. Applied sub-neg0.5

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

  8. Applied distribute-lft-in0.5

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

  9. Applied associate-+r+0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019171 
(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))))))