Average Error: 11.7 → 11.7
Time: 29.9s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.929707136934608 \cdot 10^{-249}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{elif}\;b \le 7.525919208168165 \cdot 10^{-236}:\\ \;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(c \cdot t - y \cdot i\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot z - a \cdot i\right) \cdot \sqrt{b}\right) \cdot \sqrt{b}\right)\\ \end{array}\]
\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 -3.929707136934608 \cdot 10^{-249}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\

\mathbf{elif}\;b \le 7.525919208168165 \cdot 10^{-236}:\\
\;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(c \cdot t - y \cdot i\right) \cdot j\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r28313822 = x;
        double r28313823 = y;
        double r28313824 = z;
        double r28313825 = r28313823 * r28313824;
        double r28313826 = t;
        double r28313827 = a;
        double r28313828 = r28313826 * r28313827;
        double r28313829 = r28313825 - r28313828;
        double r28313830 = r28313822 * r28313829;
        double r28313831 = b;
        double r28313832 = c;
        double r28313833 = r28313832 * r28313824;
        double r28313834 = i;
        double r28313835 = r28313834 * r28313827;
        double r28313836 = r28313833 - r28313835;
        double r28313837 = r28313831 * r28313836;
        double r28313838 = r28313830 - r28313837;
        double r28313839 = j;
        double r28313840 = r28313832 * r28313826;
        double r28313841 = r28313834 * r28313823;
        double r28313842 = r28313840 - r28313841;
        double r28313843 = r28313839 * r28313842;
        double r28313844 = r28313838 + r28313843;
        return r28313844;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r28313845 = b;
        double r28313846 = -3.929707136934608e-249;
        bool r28313847 = r28313845 <= r28313846;
        double r28313848 = c;
        double r28313849 = t;
        double r28313850 = r28313848 * r28313849;
        double r28313851 = y;
        double r28313852 = i;
        double r28313853 = r28313851 * r28313852;
        double r28313854 = r28313850 - r28313853;
        double r28313855 = j;
        double r28313856 = r28313854 * r28313855;
        double r28313857 = z;
        double r28313858 = r28313851 * r28313857;
        double r28313859 = a;
        double r28313860 = r28313849 * r28313859;
        double r28313861 = r28313858 - r28313860;
        double r28313862 = x;
        double r28313863 = r28313861 * r28313862;
        double r28313864 = cbrt(r28313863);
        double r28313865 = r28313864 * r28313864;
        double r28313866 = r28313865 * r28313864;
        double r28313867 = r28313848 * r28313857;
        double r28313868 = r28313859 * r28313852;
        double r28313869 = r28313867 - r28313868;
        double r28313870 = r28313845 * r28313869;
        double r28313871 = r28313866 - r28313870;
        double r28313872 = r28313856 + r28313871;
        double r28313873 = 7.525919208168165e-236;
        bool r28313874 = r28313845 <= r28313873;
        double r28313875 = r28313863 + r28313856;
        double r28313876 = sqrt(r28313845);
        double r28313877 = r28313869 * r28313876;
        double r28313878 = r28313877 * r28313876;
        double r28313879 = r28313863 - r28313878;
        double r28313880 = r28313856 + r28313879;
        double r28313881 = r28313874 ? r28313875 : r28313880;
        double r28313882 = r28313847 ? r28313872 : r28313881;
        return r28313882;
}

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

Target

Original11.7
Target15.6
Herbie11.7
\[\begin{array}{l} \mathbf{if}\;t \lt -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -3.929707136934608e-249

    1. Initial program 10.9

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

    3. Applied add-cube-cbrt11.2

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

    if -3.929707136934608e-249 < b < 7.525919208168165e-236

    1. Initial program 18.1

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

    2. Taylor expanded around 0 16.7

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{0}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if 7.525919208168165e-236 < b

    1. Initial program 10.4

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

    3. Applied add-sqr-sqrt10.5

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

    4. Applied associate-*l*10.5

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

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.929707136934608 \cdot 10^{-249}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{elif}\;b \le 7.525919208168165 \cdot 10^{-236}:\\ \;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(c \cdot t - y \cdot i\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot z - a \cdot i\right) \cdot \sqrt{b}\right) \cdot \sqrt{b}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))