Average Error: 4.9 → 4.9
Time: 24.3s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\left(b \cdot c - \left(4.0 \cdot \left(i \cdot x\right) + \sqrt{27.0} \cdot \left(\sqrt{27.0} \cdot \left(k \cdot j\right)\right)\right)\right) + t \cdot \left(\left(z \cdot x\right) \cdot \left(18.0 \cdot y\right) - 4.0 \cdot a\right)\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\left(b \cdot c - \left(4.0 \cdot \left(i \cdot x\right) + \sqrt{27.0} \cdot \left(\sqrt{27.0} \cdot \left(k \cdot j\right)\right)\right)\right) + t \cdot \left(\left(z \cdot x\right) \cdot \left(18.0 \cdot y\right) - 4.0 \cdot a\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r4538876 = x;
        double r4538877 = 18.0;
        double r4538878 = r4538876 * r4538877;
        double r4538879 = y;
        double r4538880 = r4538878 * r4538879;
        double r4538881 = z;
        double r4538882 = r4538880 * r4538881;
        double r4538883 = t;
        double r4538884 = r4538882 * r4538883;
        double r4538885 = a;
        double r4538886 = 4.0;
        double r4538887 = r4538885 * r4538886;
        double r4538888 = r4538887 * r4538883;
        double r4538889 = r4538884 - r4538888;
        double r4538890 = b;
        double r4538891 = c;
        double r4538892 = r4538890 * r4538891;
        double r4538893 = r4538889 + r4538892;
        double r4538894 = r4538876 * r4538886;
        double r4538895 = i;
        double r4538896 = r4538894 * r4538895;
        double r4538897 = r4538893 - r4538896;
        double r4538898 = j;
        double r4538899 = 27.0;
        double r4538900 = r4538898 * r4538899;
        double r4538901 = k;
        double r4538902 = r4538900 * r4538901;
        double r4538903 = r4538897 - r4538902;
        return r4538903;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r4538904 = b;
        double r4538905 = c;
        double r4538906 = r4538904 * r4538905;
        double r4538907 = 4.0;
        double r4538908 = i;
        double r4538909 = x;
        double r4538910 = r4538908 * r4538909;
        double r4538911 = r4538907 * r4538910;
        double r4538912 = 27.0;
        double r4538913 = sqrt(r4538912);
        double r4538914 = k;
        double r4538915 = j;
        double r4538916 = r4538914 * r4538915;
        double r4538917 = r4538913 * r4538916;
        double r4538918 = r4538913 * r4538917;
        double r4538919 = r4538911 + r4538918;
        double r4538920 = r4538906 - r4538919;
        double r4538921 = t;
        double r4538922 = z;
        double r4538923 = r4538922 * r4538909;
        double r4538924 = 18.0;
        double r4538925 = y;
        double r4538926 = r4538924 * r4538925;
        double r4538927 = r4538923 * r4538926;
        double r4538928 = a;
        double r4538929 = r4538907 * r4538928;
        double r4538930 = r4538927 - r4538929;
        double r4538931 = r4538921 * r4538930;
        double r4538932 = r4538920 + r4538931;
        return r4538932;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.9

    \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

  2. Simplified5.0

    \[\leadsto \color{blue}{\left(b \cdot c - \left(k \cdot \left(j \cdot 27.0\right) + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\left(y \cdot x\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot t}\]

  3. Taylor expanded around inf 5.8

    \[\leadsto \left(b \cdot c - \left(k \cdot \left(j \cdot 27.0\right) + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\color{blue}{18.0 \cdot \left(x \cdot \left(z \cdot y\right)\right)} - a \cdot 4.0\right) \cdot t\]

  4. Taylor expanded around inf 5.7

    \[\leadsto \left(b \cdot c - \left(k \cdot \left(j \cdot 27.0\right) + \left(i \cdot x\right) \cdot 4.0\right)\right) + \color{blue}{\left(18.0 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) - 4.0 \cdot \left(t \cdot a\right)\right)}\]

  5. Simplified5.0

    \[\leadsto \left(b \cdot c - \left(k \cdot \left(j \cdot 27.0\right) + \left(i \cdot x\right) \cdot 4.0\right)\right) + \color{blue}{t \cdot \left(\left(18.0 \cdot y\right) \cdot \left(x \cdot z\right) - 4.0 \cdot a\right)}\]
  6. Using strategy rm

  7. Applied associate-*r*4.9

    \[\leadsto \left(b \cdot c - \left(\color{blue}{\left(k \cdot j\right) \cdot 27.0} + \left(i \cdot x\right) \cdot 4.0\right)\right) + t \cdot \left(\left(18.0 \cdot y\right) \cdot \left(x \cdot z\right) - 4.0 \cdot a\right)\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt4.9

    \[\leadsto \left(b \cdot c - \left(\left(k \cdot j\right) \cdot \color{blue}{\left(\sqrt{27.0} \cdot \sqrt{27.0}\right)} + \left(i \cdot x\right) \cdot 4.0\right)\right) + t \cdot \left(\left(18.0 \cdot y\right) \cdot \left(x \cdot z\right) - 4.0 \cdot a\right)\]

  10. Applied associate-*r*4.9

    \[\leadsto \left(b \cdot c - \left(\color{blue}{\left(\left(k \cdot j\right) \cdot \sqrt{27.0}\right) \cdot \sqrt{27.0}} + \left(i \cdot x\right) \cdot 4.0\right)\right) + t \cdot \left(\left(18.0 \cdot y\right) \cdot \left(x \cdot z\right) - 4.0 \cdot a\right)\]

  11. Final simplification4.9

    \[\leadsto \left(b \cdot c - \left(4.0 \cdot \left(i \cdot x\right) + \sqrt{27.0} \cdot \left(\sqrt{27.0} \cdot \left(k \cdot j\right)\right)\right)\right) + t \cdot \left(\left(z \cdot x\right) \cdot \left(18.0 \cdot y\right) - 4.0 \cdot a\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))