Average Error: 0.6 → 0.5
Time: 24.1s
Precision: 64
\[4 \le x1 \le 6.36000000000000032 \land 4 \le x2 \le 6.36000000000000032 \land 4 \le x3 \le 6.36000000000000032 \land 4 \le x4 \le 6.36000000000000032 \land 4 \le x5 \le 6.36000000000000032 \land 4 \le x6 \le 6.36000000000000032\]
\[\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)\]
\[\left(\frac{\left({\left(x2 - x1\right)}^{3} + {\left(\left(x3 - x4\right) + x5\right)}^{3}\right) \cdot x1}{\left(x2 - x1\right) \cdot \left(x2 - x1\right) + \left(\left(\left(x3 - x4\right) + x5\right) \cdot \left(\left(x3 - x4\right) + x5\right) - \left(x2 - x1\right) \cdot \left(\left(x3 - x4\right) + x5\right)\right)} + \left(x6 \cdot x1 + x3 \cdot \left(x6 - x2\right)\right)\right) + x5 \cdot \left(x2 - x6\right)\]
\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)
\left(\frac{\left({\left(x2 - x1\right)}^{3} + {\left(\left(x3 - x4\right) + x5\right)}^{3}\right) \cdot x1}{\left(x2 - x1\right) \cdot \left(x2 - x1\right) + \left(\left(\left(x3 - x4\right) + x5\right) \cdot \left(\left(x3 - x4\right) + x5\right) - \left(x2 - x1\right) \cdot \left(\left(x3 - x4\right) + x5\right)\right)} + \left(x6 \cdot x1 + x3 \cdot \left(x6 - x2\right)\right)\right) + x5 \cdot \left(x2 - x6\right)
double f(double x1, double x2, double x3, double x4, double x5, double x6) {
        double r164894 = x2;
        double r164895 = x5;
        double r164896 = r164894 * r164895;
        double r164897 = x3;
        double r164898 = x6;
        double r164899 = r164897 * r164898;
        double r164900 = r164896 + r164899;
        double r164901 = r164894 * r164897;
        double r164902 = r164900 - r164901;
        double r164903 = r164895 * r164898;
        double r164904 = r164902 - r164903;
        double r164905 = x1;
        double r164906 = -r164905;
        double r164907 = r164906 + r164894;
        double r164908 = r164907 + r164897;
        double r164909 = x4;
        double r164910 = r164908 - r164909;
        double r164911 = r164910 + r164895;
        double r164912 = r164911 + r164898;
        double r164913 = r164905 * r164912;
        double r164914 = r164904 + r164913;
        return r164914;
}

double f(double x1, double x2, double x3, double x4, double x5, double x6) {
        double r164915 = x2;
        double r164916 = x1;
        double r164917 = r164915 - r164916;
        double r164918 = 3.0;
        double r164919 = pow(r164917, r164918);
        double r164920 = x3;
        double r164921 = x4;
        double r164922 = r164920 - r164921;
        double r164923 = x5;
        double r164924 = r164922 + r164923;
        double r164925 = pow(r164924, r164918);
        double r164926 = r164919 + r164925;
        double r164927 = r164926 * r164916;
        double r164928 = r164917 * r164917;
        double r164929 = r164924 * r164924;
        double r164930 = r164917 * r164924;
        double r164931 = r164929 - r164930;
        double r164932 = r164928 + r164931;
        double r164933 = r164927 / r164932;
        double r164934 = x6;
        double r164935 = r164934 * r164916;
        double r164936 = r164934 - r164915;
        double r164937 = r164920 * r164936;
        double r164938 = r164935 + r164937;
        double r164939 = r164933 + r164938;
        double r164940 = r164915 - r164934;
        double r164941 = r164923 * r164940;
        double r164942 = r164939 + r164941;
        return r164942;
}

Error

Bits error versus x1

Bits error versus x2

Bits error versus x3

Bits error versus x4

Bits error versus x5

Bits error versus x6

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)\]
  2. Simplified0.5

    \[\leadsto \color{blue}{\left(x1 \cdot \left(\left(\left(x2 - x1\right) + \left(\left(x3 - x4\right) + x5\right)\right) + x6\right) + x3 \cdot \left(x6 - x2\right)\right) + x5 \cdot \left(x2 - x6\right)}\]
  3. Using strategy rm
  4. Applied distribute-rgt-in0.4

    \[\leadsto \left(\color{blue}{\left(\left(\left(x2 - x1\right) + \left(\left(x3 - x4\right) + x5\right)\right) \cdot x1 + x6 \cdot x1\right)} + x3 \cdot \left(x6 - x2\right)\right) + x5 \cdot \left(x2 - x6\right)\]
  5. Applied associate-+l+0.4

    \[\leadsto \color{blue}{\left(\left(\left(x2 - x1\right) + \left(\left(x3 - x4\right) + x5\right)\right) \cdot x1 + \left(x6 \cdot x1 + x3 \cdot \left(x6 - x2\right)\right)\right)} + x5 \cdot \left(x2 - x6\right)\]
  6. Using strategy rm
  7. Applied flip3-+0.5

    \[\leadsto \left(\color{blue}{\frac{{\left(x2 - x1\right)}^{3} + {\left(\left(x3 - x4\right) + x5\right)}^{3}}{\left(x2 - x1\right) \cdot \left(x2 - x1\right) + \left(\left(\left(x3 - x4\right) + x5\right) \cdot \left(\left(x3 - x4\right) + x5\right) - \left(x2 - x1\right) \cdot \left(\left(x3 - x4\right) + x5\right)\right)}} \cdot x1 + \left(x6 \cdot x1 + x3 \cdot \left(x6 - x2\right)\right)\right) + x5 \cdot \left(x2 - x6\right)\]
  8. Applied associate-*l/0.5

    \[\leadsto \left(\color{blue}{\frac{\left({\left(x2 - x1\right)}^{3} + {\left(\left(x3 - x4\right) + x5\right)}^{3}\right) \cdot x1}{\left(x2 - x1\right) \cdot \left(x2 - x1\right) + \left(\left(\left(x3 - x4\right) + x5\right) \cdot \left(\left(x3 - x4\right) + x5\right) - \left(x2 - x1\right) \cdot \left(\left(x3 - x4\right) + x5\right)\right)}} + \left(x6 \cdot x1 + x3 \cdot \left(x6 - x2\right)\right)\right) + x5 \cdot \left(x2 - x6\right)\]
  9. Final simplification0.5

    \[\leadsto \left(\frac{\left({\left(x2 - x1\right)}^{3} + {\left(\left(x3 - x4\right) + x5\right)}^{3}\right) \cdot x1}{\left(x2 - x1\right) \cdot \left(x2 - x1\right) + \left(\left(\left(x3 - x4\right) + x5\right) \cdot \left(\left(x3 - x4\right) + x5\right) - \left(x2 - x1\right) \cdot \left(\left(x3 - x4\right) + x5\right)\right)} + \left(x6 \cdot x1 + x3 \cdot \left(x6 - x2\right)\right)\right) + x5 \cdot \left(x2 - x6\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x1 x2 x3 x4 x5 x6)
  :name "kepler0"
  :pre (and (<= 4.0 x1 6.36) (<= 4.0 x2 6.36) (<= 4.0 x3 6.36) (<= 4.0 x4 6.36) (<= 4.0 x5 6.36) (<= 4.0 x6 6.36))
  (+ (- (- (+ (* x2 x5) (* x3 x6)) (* x2 x3)) (* x5 x6)) (* x1 (+ (+ (- (+ (+ (- x1) x2) x3) x4) x5) x6))))