Average Error: 11.2 → 9.1
Time: 27.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.7988923798283882 \cdot 10^{+75}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(\sqrt[3]{b} \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\\ \mathbf{elif}\;b \le 1.205607812754414 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot \left(z \cdot y - t \cdot a\right) - \left(\left(-i \cdot \left(b \cdot a\right)\right) + \left(c \cdot b\right) \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(\sqrt[3]{b} \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\\ \end{array}\]
\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)
↓
\begin{array}{l}
\mathbf{if}\;b \le -1.7988923798283882 \cdot 10^{+75}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(\sqrt[3]{b} \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\\

\mathbf{elif}\;b \le 1.205607812754414 \cdot 10^{+86}:\\
\;\;\;\;\left(x \cdot \left(z \cdot y - t \cdot a\right) - \left(\left(-i \cdot \left(b \cdot a\right)\right) + \left(c \cdot b\right) \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(\sqrt[3]{b} \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4632058 = x;
        double r4632059 = y;
        double r4632060 = z;
        double r4632061 = r4632059 * r4632060;
        double r4632062 = t;
        double r4632063 = a;
        double r4632064 = r4632062 * r4632063;
        double r4632065 = r4632061 - r4632064;
        double r4632066 = r4632058 * r4632065;
        double r4632067 = b;
        double r4632068 = c;
        double r4632069 = r4632068 * r4632060;
        double r4632070 = i;
        double r4632071 = r4632070 * r4632063;
        double r4632072 = r4632069 - r4632071;
        double r4632073 = r4632067 * r4632072;
        double r4632074 = r4632066 - r4632073;
        double r4632075 = j;
        double r4632076 = r4632068 * r4632062;
        double r4632077 = r4632070 * r4632059;
        double r4632078 = r4632076 - r4632077;
        double r4632079 = r4632075 * r4632078;
        double r4632080 = r4632074 + r4632079;
        return r4632080;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4632081 = b;
        double r4632082 = -1.7988923798283882e+75;
        bool r4632083 = r4632081 <= r4632082;
        double r4632084 = j;
        double r4632085 = t;
        double r4632086 = c;
        double r4632087 = r4632085 * r4632086;
        double r4632088 = y;
        double r4632089 = i;
        double r4632090 = r4632088 * r4632089;
        double r4632091 = r4632087 - r4632090;
        double r4632092 = r4632084 * r4632091;
        double r4632093 = x;
        double r4632094 = z;
        double r4632095 = r4632094 * r4632088;
        double r4632096 = r4632093 * r4632095;
        double r4632097 = a;
        double r4632098 = r4632093 * r4632085;
        double r4632099 = r4632097 * r4632098;
        double r4632100 = r4632096 - r4632099;
        double r4632101 = cbrt(r4632081);
        double r4632102 = r4632094 * r4632086;
        double r4632103 = r4632097 * r4632089;
        double r4632104 = r4632102 - r4632103;
        double r4632105 = r4632101 * r4632104;
        double r4632106 = r4632101 * r4632101;
        double r4632107 = r4632105 * r4632106;
        double r4632108 = r4632100 - r4632107;
        double r4632109 = r4632092 + r4632108;
        double r4632110 = 1.205607812754414e+86;
        bool r4632111 = r4632081 <= r4632110;
        double r4632112 = r4632085 * r4632097;
        double r4632113 = r4632095 - r4632112;
        double r4632114 = r4632093 * r4632113;
        double r4632115 = r4632081 * r4632097;
        double r4632116 = r4632089 * r4632115;
        double r4632117 = -r4632116;
        double r4632118 = r4632086 * r4632081;
        double r4632119 = r4632118 * r4632094;
        double r4632120 = r4632117 + r4632119;
        double r4632121 = r4632114 - r4632120;
        double r4632122 = r4632121 + r4632092;
        double r4632123 = r4632111 ? r4632122 : r4632109;
        double r4632124 = r4632083 ? r4632109 : r4632123;
        return r4632124;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if b < -1.7988923798283882e+75 or 1.205607812754414e+86 < b

    1. Initial program 6.4

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt6.9

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    4. Applied associate-*l*6.9

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    5. Taylor expanded around inf 7.7

      \[\leadsto \left(\color{blue}{\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right)} - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(c \cdot z - i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if -1.7988923798283882e+75 < b < 1.205607812754414e+86

    1. Initial program 12.8

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt13.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    4. Applied associate-*l*13.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    5. Using strategy rm

    6. Applied sub-neg13.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    7. Applied distribute-lft-in13.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \color{blue}{\left(\sqrt[3]{b} \cdot \left(c \cdot z\right) + \sqrt[3]{b} \cdot \left(-i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    8. Applied distribute-lft-in13.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(c \cdot z\right)\right) + \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(-i \cdot a\right)\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    9. Simplified11.3

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{c \cdot \left(z \cdot b\right)} + \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(-i \cdot a\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    10. Simplified9.5

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

    11. Taylor expanded around inf 9.5

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(c \cdot \left(z \cdot b\right) + \color{blue}{-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    12. Simplified9.4

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

    13. Taylor expanded around inf 9.5

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{z \cdot \left(b \cdot c\right)} + \left(a \cdot b\right) \cdot \left(-i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.7988923798283882 \cdot 10^{+75}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(\sqrt[3]{b} \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\\ \mathbf{elif}\;b \le 1.205607812754414 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot \left(z \cdot y - t \cdot a\right) - \left(\left(-i \cdot \left(b \cdot a\right)\right) + \left(c \cdot b\right) \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(x \cdot \left(z \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - \left(\sqrt[3]{b} \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))