Average Error: 12.4 → 9.6
Time: 7.5s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.31775490019201837 \cdot 10^{84} \lor \neg \left(b \le 4954531051790429180\right):\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + 1 \cdot \left(-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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 -3.31775490019201837 \cdot 10^{84} \lor \neg \left(b \le 4954531051790429180\right):\\
\;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(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(-1 \cdot \left(a \cdot \left(i \cdot b\right)\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 r659906 = x;
        double r659907 = y;
        double r659908 = z;
        double r659909 = r659907 * r659908;
        double r659910 = t;
        double r659911 = a;
        double r659912 = r659910 * r659911;
        double r659913 = r659909 - r659912;
        double r659914 = r659906 * r659913;
        double r659915 = b;
        double r659916 = c;
        double r659917 = r659916 * r659908;
        double r659918 = i;
        double r659919 = r659918 * r659911;
        double r659920 = r659917 - r659919;
        double r659921 = r659915 * r659920;
        double r659922 = r659914 - r659921;
        double r659923 = j;
        double r659924 = r659916 * r659910;
        double r659925 = r659918 * r659907;
        double r659926 = r659924 - r659925;
        double r659927 = r659923 * r659926;
        double r659928 = r659922 + r659927;
        return r659928;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r659929 = b;
        double r659930 = -3.3177549001920184e+84;
        bool r659931 = r659929 <= r659930;
        double r659932 = 4.954531051790429e+18;
        bool r659933 = r659929 <= r659932;
        double r659934 = !r659933;
        bool r659935 = r659931 || r659934;
        double r659936 = x;
        double r659937 = y;
        double r659938 = z;
        double r659939 = r659937 * r659938;
        double r659940 = t;
        double r659941 = a;
        double r659942 = r659940 * r659941;
        double r659943 = r659939 - r659942;
        double r659944 = cbrt(r659943);
        double r659945 = r659944 * r659944;
        double r659946 = r659936 * r659945;
        double r659947 = r659946 * r659944;
        double r659948 = c;
        double r659949 = r659948 * r659938;
        double r659950 = i;
        double r659951 = r659950 * r659941;
        double r659952 = r659949 - r659951;
        double r659953 = r659929 * r659952;
        double r659954 = r659947 - r659953;
        double r659955 = j;
        double r659956 = r659948 * r659940;
        double r659957 = r659950 * r659937;
        double r659958 = r659956 - r659957;
        double r659959 = r659955 * r659958;
        double r659960 = r659954 + r659959;
        double r659961 = r659936 * r659943;
        double r659962 = r659929 * r659948;
        double r659963 = r659962 * r659938;
        double r659964 = 1.0;
        double r659965 = -1.0;
        double r659966 = r659950 * r659929;
        double r659967 = r659941 * r659966;
        double r659968 = r659965 * r659967;
        double r659969 = r659964 * r659968;
        double r659970 = r659963 + r659969;
        double r659971 = r659961 - r659970;
        double r659972 = r659971 + r659959;
        double r659973 = r659935 ? r659960 : r659972;
        return r659973;
}

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

Original12.4
Target16.1
Herbie9.6
\[\begin{array}{l} \mathbf{if}\;t \lt -8.1209789191959122 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.7125538182184851 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.63353334603158369 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -3.3177549001920184e+84 or 4.954531051790429e+18 < b

    1. Initial program 7.3

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

    3. Applied add-cube-cbrt7.5

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

    4. Applied associate-*r*7.5

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

    if -3.3177549001920184e+84 < b < 4.954531051790429e+18

    1. Initial program 14.7

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

    3. Applied sub-neg14.7

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

    4. Applied distribute-lft-in14.7

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

    6. Applied *-un-lft-identity14.7

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

    7. Applied associate-*l*14.7

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

    8. Simplified12.5

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

    10. Applied associate-*r*10.5

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

  4. Final simplification9.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.31775490019201837 \cdot 10^{84} \lor \neg \left(b \le 4954531051790429180\right):\\ \;\;\;\;\left(\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + 1 \cdot \left(-1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

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

  :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)))))