Average Error: 11.9 → 9.0
Time: 13.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -5.2181879849637582 \cdot 10^{-18} \lor \neg \left(a \le 1844845652774962940\right):\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\left(-i \cdot \left(j \cdot y\right)\right) + \left(a \cdot j\right) \cdot c\right)\\ \end{array}\]
\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)
↓
\begin{array}{l}
\mathbf{if}\;a \le -5.2181879849637582 \cdot 10^{-18} \lor \neg \left(a \le 1844845652774962940\right):\\
\;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1577778 = x;
        double r1577779 = y;
        double r1577780 = z;
        double r1577781 = r1577779 * r1577780;
        double r1577782 = t;
        double r1577783 = a;
        double r1577784 = r1577782 * r1577783;
        double r1577785 = r1577781 - r1577784;
        double r1577786 = r1577778 * r1577785;
        double r1577787 = b;
        double r1577788 = c;
        double r1577789 = r1577788 * r1577780;
        double r1577790 = i;
        double r1577791 = r1577782 * r1577790;
        double r1577792 = r1577789 - r1577791;
        double r1577793 = r1577787 * r1577792;
        double r1577794 = r1577786 - r1577793;
        double r1577795 = j;
        double r1577796 = r1577788 * r1577783;
        double r1577797 = r1577779 * r1577790;
        double r1577798 = r1577796 - r1577797;
        double r1577799 = r1577795 * r1577798;
        double r1577800 = r1577794 + r1577799;
        return r1577800;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1577801 = a;
        double r1577802 = -5.218187984963758e-18;
        bool r1577803 = r1577801 <= r1577802;
        double r1577804 = 1.844845652774963e+18;
        bool r1577805 = r1577801 <= r1577804;
        double r1577806 = !r1577805;
        bool r1577807 = r1577803 || r1577806;
        double r1577808 = x;
        double r1577809 = z;
        double r1577810 = y;
        double r1577811 = r1577809 * r1577810;
        double r1577812 = r1577808 * r1577811;
        double r1577813 = t;
        double r1577814 = r1577808 * r1577813;
        double r1577815 = r1577801 * r1577814;
        double r1577816 = -r1577815;
        double r1577817 = r1577812 + r1577816;
        double r1577818 = b;
        double r1577819 = c;
        double r1577820 = r1577819 * r1577809;
        double r1577821 = i;
        double r1577822 = r1577813 * r1577821;
        double r1577823 = r1577820 - r1577822;
        double r1577824 = r1577818 * r1577823;
        double r1577825 = r1577817 - r1577824;
        double r1577826 = j;
        double r1577827 = r1577826 * r1577819;
        double r1577828 = r1577801 * r1577827;
        double r1577829 = r1577810 * r1577821;
        double r1577830 = -r1577829;
        double r1577831 = r1577830 * r1577826;
        double r1577832 = r1577828 + r1577831;
        double r1577833 = r1577825 + r1577832;
        double r1577834 = r1577810 * r1577809;
        double r1577835 = r1577813 * r1577801;
        double r1577836 = r1577834 - r1577835;
        double r1577837 = r1577808 * r1577836;
        double r1577838 = r1577837 - r1577824;
        double r1577839 = r1577826 * r1577810;
        double r1577840 = r1577821 * r1577839;
        double r1577841 = -r1577840;
        double r1577842 = r1577801 * r1577826;
        double r1577843 = r1577842 * r1577819;
        double r1577844 = r1577841 + r1577843;
        double r1577845 = r1577838 + r1577844;
        double r1577846 = r1577807 ? r1577833 : r1577845;
        return r1577846;
}

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

Original11.9
Target19.8
Herbie9.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.46969429677770502 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -5.218187984963758e-18 or 1.844845652774963e+18 < a

    1. Initial program 16.7

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

    3. Applied sub-neg16.7

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

    4. Applied distribute-lft-in16.7

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

    5. Simplified12.7

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

    6. Simplified12.7

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

    8. Applied sub-neg12.7

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

    9. Applied distribute-lft-in12.7

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

    10. Simplified12.7

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

    11. Simplified8.4

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

    if -5.218187984963758e-18 < a < 1.844845652774963e+18

    1. Initial program 8.8

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

    3. Applied sub-neg8.8

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

    4. Applied distribute-lft-in8.8

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

    5. Simplified12.2

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

    6. Simplified12.2

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

    8. Applied neg-mul-112.2

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

    9. Applied associate-*l*12.2

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

    10. Simplified12.2

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

    12. Applied associate-*r*9.4

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

  4. Final simplification9.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -5.2181879849637582 \cdot 10^{-18} \lor \neg \left(a \le 1844845652774962940\right):\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-y \cdot i\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(\left(-i \cdot \left(j \cdot y\right)\right) + \left(a \cdot j\right) \cdot c\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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