Average Error: 11.7 → 9.2
Time: 29.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -7.642798871419527 \cdot 10^{+20}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot t} \cdot \sqrt[3]{z \cdot c - i \cdot t}\right)\right) \cdot \sqrt[3]{z \cdot c - i \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;j \le 6.910480137132264 \cdot 10^{+91}:\\ \;\;\;\;\left(c \cdot \left(j \cdot a\right) + \left(i \cdot j\right) \cdot \left(-y\right)\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - i \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - i \cdot t\right)\right) + \sqrt{j} \cdot \left(\left(c \cdot a - y \cdot i\right) \cdot \sqrt{j}\right)\\ \end{array}\]
\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}\;j \le -7.642798871419527 \cdot 10^{+20}:\\
\;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot t} \cdot \sqrt[3]{z \cdot c - i \cdot t}\right)\right) \cdot \sqrt[3]{z \cdot c - i \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\

\mathbf{elif}\;j \le 6.910480137132264 \cdot 10^{+91}:\\
\;\;\;\;\left(c \cdot \left(j \cdot a\right) + \left(i \cdot j\right) \cdot \left(-y\right)\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - i \cdot t\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r39060955 = x;
        double r39060956 = y;
        double r39060957 = z;
        double r39060958 = r39060956 * r39060957;
        double r39060959 = t;
        double r39060960 = a;
        double r39060961 = r39060959 * r39060960;
        double r39060962 = r39060958 - r39060961;
        double r39060963 = r39060955 * r39060962;
        double r39060964 = b;
        double r39060965 = c;
        double r39060966 = r39060965 * r39060957;
        double r39060967 = i;
        double r39060968 = r39060959 * r39060967;
        double r39060969 = r39060966 - r39060968;
        double r39060970 = r39060964 * r39060969;
        double r39060971 = r39060963 - r39060970;
        double r39060972 = j;
        double r39060973 = r39060965 * r39060960;
        double r39060974 = r39060956 * r39060967;
        double r39060975 = r39060973 - r39060974;
        double r39060976 = r39060972 * r39060975;
        double r39060977 = r39060971 + r39060976;
        return r39060977;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r39060978 = j;
        double r39060979 = -7.642798871419527e+20;
        bool r39060980 = r39060978 <= r39060979;
        double r39060981 = y;
        double r39060982 = z;
        double r39060983 = r39060981 * r39060982;
        double r39060984 = t;
        double r39060985 = a;
        double r39060986 = r39060984 * r39060985;
        double r39060987 = r39060983 - r39060986;
        double r39060988 = x;
        double r39060989 = r39060987 * r39060988;
        double r39060990 = b;
        double r39060991 = c;
        double r39060992 = r39060982 * r39060991;
        double r39060993 = i;
        double r39060994 = r39060993 * r39060984;
        double r39060995 = r39060992 - r39060994;
        double r39060996 = cbrt(r39060995);
        double r39060997 = r39060996 * r39060996;
        double r39060998 = r39060990 * r39060997;
        double r39060999 = r39060998 * r39060996;
        double r39061000 = r39060989 - r39060999;
        double r39061001 = r39060991 * r39060985;
        double r39061002 = r39060981 * r39060993;
        double r39061003 = r39061001 - r39061002;
        double r39061004 = r39060978 * r39061003;
        double r39061005 = r39061000 + r39061004;
        double r39061006 = 6.910480137132264e+91;
        bool r39061007 = r39060978 <= r39061006;
        double r39061008 = r39060978 * r39060985;
        double r39061009 = r39060991 * r39061008;
        double r39061010 = r39060993 * r39060978;
        double r39061011 = -r39060981;
        double r39061012 = r39061010 * r39061011;
        double r39061013 = r39061009 + r39061012;
        double r39061014 = r39060990 * r39060995;
        double r39061015 = r39060989 - r39061014;
        double r39061016 = r39061013 + r39061015;
        double r39061017 = sqrt(r39060978);
        double r39061018 = r39061003 * r39061017;
        double r39061019 = r39061017 * r39061018;
        double r39061020 = r39061015 + r39061019;
        double r39061021 = r39061007 ? r39061016 : r39061020;
        double r39061022 = r39060980 ? r39061005 : r39061021;
        return r39061022;
}

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
Target18.4
Herbie9.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if j < -7.642798871419527e+20

    1. Initial program 7.0

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

    3. Applied add-cube-cbrt7.2

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

    4. Applied associate-*r*7.2

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

    if -7.642798871419527e+20 < j < 6.910480137132264e+91

    1. Initial program 13.7

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

    3. Applied add-cube-cbrt13.9

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

    4. Applied associate-*l*13.9

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

    6. Applied sub-neg13.9

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

    7. Applied distribute-lft-in13.9

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

    8. Applied distribute-lft-in13.9

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

    9. Simplified13.8

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

    10. Simplified11.8

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

    12. Applied associate-*l*10.1

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

    if 6.910480137132264e+91 < j

    1. Initial program 7.0

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

    3. Applied add-sqr-sqrt7.2

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

    4. Applied associate-*l*7.2

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

  4. Final simplification9.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -7.642798871419527 \cdot 10^{+20}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(b \cdot \left(\sqrt[3]{z \cdot c - i \cdot t} \cdot \sqrt[3]{z \cdot c - i \cdot t}\right)\right) \cdot \sqrt[3]{z \cdot c - i \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;j \le 6.910480137132264 \cdot 10^{+91}:\\ \;\;\;\;\left(c \cdot \left(j \cdot a\right) + \left(i \cdot j\right) \cdot \left(-y\right)\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - i \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z - t \cdot a\right) \cdot x - b \cdot \left(z \cdot c - i \cdot t\right)\right) + \sqrt{j} \cdot \left(\left(c \cdot a - y \cdot i\right) \cdot \sqrt{j}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(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) (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)))))