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;
}



# Try it out

Results

 In Out
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))))