Average Error: 12.4 → 9.8
Time: 7.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -6.2838196173283195 \cdot 10^{123} \lor \neg \left(b \le 904684009115.72681\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -6.2838196173283195 \cdot 10^{123} \lor \neg \left(b \le 904684009115.72681\right):\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\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) - \left(\left(b \cdot c\right) \cdot z + -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r120989 = x;
        double r120990 = y;
        double r120991 = z;
        double r120992 = r120990 * r120991;
        double r120993 = t;
        double r120994 = a;
        double r120995 = r120993 * r120994;
        double r120996 = r120992 - r120995;
        double r120997 = r120989 * r120996;
        double r120998 = b;
        double r120999 = c;
        double r121000 = r120999 * r120991;
        double r121001 = i;
        double r121002 = r121001 * r120994;
        double r121003 = r121000 - r121002;
        double r121004 = r120998 * r121003;
        double r121005 = r120997 - r121004;
        double r121006 = j;
        double r121007 = r120999 * r120993;
        double r121008 = r121001 * r120990;
        double r121009 = r121007 - r121008;
        double r121010 = r121006 * r121009;
        double r121011 = r121005 + r121010;
        return r121011;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r121012 = b;
        double r121013 = -6.28381961732832e+123;
        bool r121014 = r121012 <= r121013;
        double r121015 = 904684009115.7268;
        bool r121016 = r121012 <= r121015;
        double r121017 = !r121016;
        bool r121018 = r121014 || r121017;
        double r121019 = x;
        double r121020 = y;
        double r121021 = z;
        double r121022 = r121020 * r121021;
        double r121023 = t;
        double r121024 = a;
        double r121025 = r121023 * r121024;
        double r121026 = r121022 - r121025;
        double r121027 = r121019 * r121026;
        double r121028 = c;
        double r121029 = r121028 * r121021;
        double r121030 = i;
        double r121031 = r121030 * r121024;
        double r121032 = r121029 - r121031;
        double r121033 = cbrt(r121032);
        double r121034 = r121033 * r121033;
        double r121035 = r121034 * r121033;
        double r121036 = r121012 * r121035;
        double r121037 = r121027 - r121036;
        double r121038 = j;
        double r121039 = r121028 * r121023;
        double r121040 = r121030 * r121020;
        double r121041 = r121039 - r121040;
        double r121042 = r121038 * r121041;
        double r121043 = r121037 + r121042;
        double r121044 = r121012 * r121028;
        double r121045 = r121044 * r121021;
        double r121046 = -1.0;
        double r121047 = r121030 * r121012;
        double r121048 = r121024 * r121047;
        double r121049 = r121046 * r121048;
        double r121050 = r121045 + r121049;
        double r121051 = r121027 - r121050;
        double r121052 = r121051 + r121042;
        double r121053 = r121018 ? r121043 : r121052;
        return r121053;
}

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 < -6.28381961732832e+123 or 904684009115.7268 < b

    1. Initial program 7.5

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

    3. Applied add-cube-cbrt8.1

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

    if -6.28381961732832e+123 < b < 904684009115.7268

    1. Initial program 14.4

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

    3. Applied sub-neg14.4

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

    4. Applied distribute-lft-in14.4

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

    5. Taylor expanded around inf 12.3

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

    7. Applied associate-*r*10.5

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

  4. Final simplification9.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.2838196173283195 \cdot 10^{123} \lor \neg \left(b \le 904684009115.72681\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)))))