Data.Colour.Matrix:determinant from colour-2.3.3, A

Average Error: 12.3 → 9.2

Time: 25.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.885820288721452747199851344770466863725 \cdot 10^{95}:\\ \;\;\;\;\left(\left(\sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} + j \cdot \left(a \cdot c - y \cdot i\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -1.758338690148164602644415584605192188924 \cdot 10^{-166}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 5.504662105172458263088453427769459127963 \cdot 10^{-251}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right) + \left(\left(\left(j \cdot c\right) \cdot a + \left(-\left(y \cdot j\right) \cdot i\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 6.454516511442097649947162038850472776326 \cdot 10^{-203}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 6.877712242978713089253008401315914491855 \cdot 10^{-78}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \sqrt[3]{z} \cdot \left(\left(c \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot b\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 60816444.42864446341991424560546875:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot i - c \cdot z\right) \cdot \sqrt{b}\right) \cdot \sqrt{b} + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r735935 = x;
        double r735936 = y;
        double r735937 = z;
        double r735938 = r735936 * r735937;
        double r735939 = t;
        double r735940 = a;
        double r735941 = r735939 * r735940;
        double r735942 = r735938 - r735941;
        double r735943 = r735935 * r735942;
        double r735944 = b;
        double r735945 = c;
        double r735946 = r735945 * r735937;
        double r735947 = i;
        double r735948 = r735939 * r735947;
        double r735949 = r735946 - r735948;
        double r735950 = r735944 * r735949;
        double r735951 = r735943 - r735950;
        double r735952 = j;
        double r735953 = r735945 * r735940;
        double r735954 = r735936 * r735947;
        double r735955 = r735953 - r735954;
        double r735956 = r735952 * r735955;
        double r735957 = r735951 + r735956;
        return r735957;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r735958 = b;
        double r735959 = -1.8858202887214527e+95;
        bool r735960 = r735958 <= r735959;
        double r735961 = y;
        double r735962 = z;
        double r735963 = r735961 * r735962;
        double r735964 = a;
        double r735965 = t;
        double r735966 = r735964 * r735965;
        double r735967 = r735963 - r735966;
        double r735968 = x;
        double r735969 = r735967 * r735968;
        double r735970 = cbrt(r735969);
        double r735971 = r735970 * r735970;
        double r735972 = r735971 * r735970;
        double r735973 = j;
        double r735974 = c;
        double r735975 = r735964 * r735974;
        double r735976 = i;
        double r735977 = r735961 * r735976;
        double r735978 = r735975 - r735977;
        double r735979 = r735973 * r735978;
        double r735980 = r735972 + r735979;
        double r735981 = r735965 * r735976;
        double r735982 = r735974 * r735962;
        double r735983 = r735981 - r735982;
        double r735984 = r735983 * r735958;
        double r735985 = r735980 + r735984;
        double r735986 = -1.7583386901481646e-166;
        bool r735987 = r735958 <= r735986;
        double r735988 = r735962 * r735968;
        double r735989 = r735988 * r735961;
        double r735990 = r735968 * r735965;
        double r735991 = r735990 * r735964;
        double r735992 = r735989 - r735991;
        double r735993 = r735973 * r735976;
        double r735994 = r735961 * r735993;
        double r735995 = -r735994;
        double r735996 = r735973 * r735964;
        double r735997 = r735974 * r735996;
        double r735998 = r735995 + r735997;
        double r735999 = r735992 + r735998;
        double r736000 = r735965 * r735958;
        double r736001 = r736000 * r735976;
        double r736002 = r735974 * r735958;
        double r736003 = r736002 * r735962;
        double r736004 = r736001 - r736003;
        double r736005 = r735999 + r736004;
        double r736006 = 5.504662105172458e-251;
        bool r736007 = r735958 <= r736006;
        double r736008 = r735973 * r735974;
        double r736009 = r736008 * r735964;
        double r736010 = r735961 * r735973;
        double r736011 = r736010 * r735976;
        double r736012 = -r736011;
        double r736013 = r736009 + r736012;
        double r736014 = r736013 + r735969;
        double r736015 = r736004 + r736014;
        double r736016 = 6.454516511442098e-203;
        bool r736017 = r735958 <= r736016;
        double r736018 = 6.877712242978713e-78;
        bool r736019 = r735958 <= r736018;
        double r736020 = cbrt(r735962);
        double r736021 = r736020 * r736020;
        double r736022 = r735974 * r736021;
        double r736023 = r736022 * r735958;
        double r736024 = r736020 * r736023;
        double r736025 = r736001 - r736024;
        double r736026 = r735979 + r735969;
        double r736027 = r736025 + r736026;
        double r736028 = 60816444.42864446;
        bool r736029 = r735958 <= r736028;
        double r736030 = sqrt(r735958);
        double r736031 = r735983 * r736030;
        double r736032 = r736031 * r736030;
        double r736033 = r736032 + r736026;
        double r736034 = r736029 ? r736005 : r736033;
        double r736035 = r736019 ? r736027 : r736034;
        double r736036 = r736017 ? r736005 : r736035;
        double r736037 = r736007 ? r736015 : r736036;
        double r736038 = r735987 ? r736005 : r736037;
        double r736039 = r735960 ? r735985 : r736038;
        return r736039;
}

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

Target

Original	12.3
Target	19.7
Herbie	9.2

\[\begin{array}{l} \mathbf{if}\;x \lt -1.469694296777705016266218530347997287942 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.21135273622268028942701600607048800714 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

1. Split input into 5 regimes

2. if b < -1.8858202887214527e+95

   1. Initial program 6.4

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

   2. Simplified 6.4

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

   4. Applied add-cube-cbrt 6.6

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

   if -1.8858202887214527e+95 < b < -1.7583386901481646e-166 or 5.504662105172458e-251 < b < 6.454516511442098e-203 or 6.877712242978713e-78 < b < 60816444.42864446

   1. Initial program 13.0

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

   2. Simplified 13.0

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

   3. Taylor expanded around inf 10.0

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

   4. Simplified 10.1

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

   5. Taylor expanded around inf 10.9

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

   6. Simplified 9.8

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

   8. Applied associate-*r* 10.1

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

   10. Applied sub-neg 10.1

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

   11. Applied distribute-lft-in 10.1

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

   12. Simplified 10.3

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

   13. Simplified 9.3

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

   if -1.7583386901481646e-166 < b < 5.504662105172458e-251

   1. Initial program 17.3

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

   2. Simplified 17.3

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

   3. Taylor expanded around inf 10.9

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

   4. Simplified 10.9

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

   6. Applied sub-neg 10.9

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

   7. Applied distribute-lft-in 10.9

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

   8. Simplified 11.9

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

   9. Simplified 10.8

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

   if 6.454516511442098e-203 < b < 6.877712242978713e-78

   1. Initial program 15.8

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

   2. Simplified 15.8

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

   3. Taylor expanded around inf 10.4

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

   4. Simplified 10.4

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

   6. Applied add-cube-cbrt 10.5

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

   7. Applied associate-*r* 10.5

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

   8. Simplified 11.5

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

   if 60816444.42864446 < b

   1. Initial program 7.2

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

   2. Simplified 7.2

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

   4. Applied add-sqr-sqrt 7.4

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

   5. Applied associate-*r* 7.4

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

   6. Simplified 7.4

      \[\leadsto \color{blue}{\left(\left(i \cdot t - z \cdot c\right) \cdot \sqrt{b}\right)} \cdot \sqrt{b} + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(z \cdot y - t \cdot a\right) \cdot x\right)\]
3. Recombined 5 regimes into one program.

4. Final simplification 9.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.885820288721452747199851344770466863725 \cdot 10^{95}:\\ \;\;\;\;\left(\left(\sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - a \cdot t\right) \cdot x} + j \cdot \left(a \cdot c - y \cdot i\right)\right) + \left(t \cdot i - c \cdot z\right) \cdot b\\ \mathbf{elif}\;b \le -1.758338690148164602644415584605192188924 \cdot 10^{-166}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 5.504662105172458263088453427769459127963 \cdot 10^{-251}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right) + \left(\left(\left(j \cdot c\right) \cdot a + \left(-\left(y \cdot j\right) \cdot i\right)\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 6.454516511442097649947162038850472776326 \cdot 10^{-203}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{elif}\;b \le 6.877712242978713089253008401315914491855 \cdot 10^{-78}:\\ \;\;\;\;\left(\left(t \cdot b\right) \cdot i - \sqrt[3]{z} \cdot \left(\left(c \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot b\right)\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \mathbf{elif}\;b \le 60816444.42864446341991424560546875:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot y - \left(x \cdot t\right) \cdot a\right) + \left(\left(-y \cdot \left(j \cdot i\right)\right) + c \cdot \left(j \cdot a\right)\right)\right) + \left(\left(t \cdot b\right) \cdot i - \left(c \cdot b\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot i - c \cdot z\right) \cdot \sqrt{b}\right) \cdot \sqrt{b} + \left(j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot z - a \cdot t\right) \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* 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) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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