Average Error: 12.0 → 10.3
Time: 7.9s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.9093385244904942 \cdot 10^{32} \lor \neg \left(a \le 9.3561614731253176 \cdot 10^{-41}\right):\\ \;\;\;\;\left(a \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + {\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right)}^{1}\right)\\ \end{array}\]
\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}\;a \le -1.9093385244904942 \cdot 10^{32} \lor \neg \left(a \le 9.3561614731253176 \cdot 10^{-41}\right):\\
\;\;\;\;\left(a \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + {\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right)}^{1}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r112047 = x;
        double r112048 = y;
        double r112049 = z;
        double r112050 = r112048 * r112049;
        double r112051 = t;
        double r112052 = a;
        double r112053 = r112051 * r112052;
        double r112054 = r112050 - r112053;
        double r112055 = r112047 * r112054;
        double r112056 = b;
        double r112057 = c;
        double r112058 = r112057 * r112049;
        double r112059 = i;
        double r112060 = r112059 * r112052;
        double r112061 = r112058 - r112060;
        double r112062 = r112056 * r112061;
        double r112063 = r112055 - r112062;
        double r112064 = j;
        double r112065 = r112057 * r112051;
        double r112066 = r112059 * r112048;
        double r112067 = r112065 - r112066;
        double r112068 = r112064 * r112067;
        double r112069 = r112063 + r112068;
        return r112069;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r112070 = a;
        double r112071 = -1.9093385244904942e+32;
        bool r112072 = r112070 <= r112071;
        double r112073 = 9.356161473125318e-41;
        bool r112074 = r112070 <= r112073;
        double r112075 = !r112074;
        bool r112076 = r112072 || r112075;
        double r112077 = i;
        double r112078 = b;
        double r112079 = r112077 * r112078;
        double r112080 = r112070 * r112079;
        double r112081 = z;
        double r112082 = c;
        double r112083 = r112078 * r112082;
        double r112084 = r112081 * r112083;
        double r112085 = x;
        double r112086 = t;
        double r112087 = r112085 * r112086;
        double r112088 = r112070 * r112087;
        double r112089 = r112084 + r112088;
        double r112090 = r112080 - r112089;
        double r112091 = j;
        double r112092 = r112082 * r112086;
        double r112093 = y;
        double r112094 = r112077 * r112093;
        double r112095 = r112092 - r112094;
        double r112096 = r112091 * r112095;
        double r112097 = r112090 + r112096;
        double r112098 = r112093 * r112081;
        double r112099 = r112086 * r112070;
        double r112100 = r112098 - r112099;
        double r112101 = r112085 * r112100;
        double r112102 = r112082 * r112081;
        double r112103 = r112077 * r112070;
        double r112104 = r112102 - r112103;
        double r112105 = r112078 * r112104;
        double r112106 = r112101 - r112105;
        double r112107 = r112091 * r112082;
        double r112108 = r112086 * r112107;
        double r112109 = -1.0;
        double r112110 = r112093 * r112091;
        double r112111 = r112077 * r112110;
        double r112112 = r112109 * r112111;
        double r112113 = 1.0;
        double r112114 = pow(r112112, r112113);
        double r112115 = r112108 + r112114;
        double r112116 = r112106 + r112115;
        double r112117 = r112076 ? r112097 : r112116;
        return r112117;
}

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 a < -1.9093385244904942e+32 or 9.356161473125318e-41 < a

    1. Initial program 16.1

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

    2. Taylor expanded around inf 13.5

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

    if -1.9093385244904942e+32 < a < 9.356161473125318e-41

    1. Initial program 9.2

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

    3. Applied add-cube-cbrt9.6

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

    4. Applied associate-*l*9.6

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

    6. Applied sub-neg9.6

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

    7. Applied distribute-lft-in9.6

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

    8. Applied distribute-lft-in9.6

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

    9. Simplified8.9

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

    10. Simplified8.7

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

    12. Applied pow18.7

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

    13. Applied pow18.7

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

    14. Applied pow-prod-down8.7

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

    15. Applied pow18.7

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

    16. Applied pow-prod-down8.7

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

    17. Simplified8.1

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + {\color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right)}}^{1}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.9093385244904942 \cdot 10^{32} \lor \neg \left(a \le 9.3561614731253176 \cdot 10^{-41}\right):\\ \;\;\;\;\left(a \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + a \cdot \left(x \cdot t\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + {\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right)}^{1}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))