Average Error: 11.3 → 11.3
Time: 35.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.645805544531443 \cdot 10^{-232}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b}\right)\right)\\ \mathbf{elif}\;x \le 2.3221986550473696 \cdot 10^{-227}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - a \cdot t\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]
\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}\;x \le -3.645805544531443 \cdot 10^{-232}:\\
\;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b}\right)\right)\\

\mathbf{elif}\;x \le 2.3221986550473696 \cdot 10^{-227}:\\
\;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - a \cdot t\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r39858744 = x;
        double r39858745 = y;
        double r39858746 = z;
        double r39858747 = r39858745 * r39858746;
        double r39858748 = t;
        double r39858749 = a;
        double r39858750 = r39858748 * r39858749;
        double r39858751 = r39858747 - r39858750;
        double r39858752 = r39858744 * r39858751;
        double r39858753 = b;
        double r39858754 = c;
        double r39858755 = r39858754 * r39858746;
        double r39858756 = i;
        double r39858757 = r39858756 * r39858749;
        double r39858758 = r39858755 - r39858757;
        double r39858759 = r39858753 * r39858758;
        double r39858760 = r39858752 - r39858759;
        double r39858761 = j;
        double r39858762 = r39858754 * r39858748;
        double r39858763 = r39858756 * r39858745;
        double r39858764 = r39858762 - r39858763;
        double r39858765 = r39858761 * r39858764;
        double r39858766 = r39858760 + r39858765;
        return r39858766;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r39858767 = x;
        double r39858768 = -3.645805544531443e-232;
        bool r39858769 = r39858767 <= r39858768;
        double r39858770 = c;
        double r39858771 = t;
        double r39858772 = r39858770 * r39858771;
        double r39858773 = i;
        double r39858774 = y;
        double r39858775 = r39858773 * r39858774;
        double r39858776 = r39858772 - r39858775;
        double r39858777 = j;
        double r39858778 = r39858776 * r39858777;
        double r39858779 = z;
        double r39858780 = r39858774 * r39858779;
        double r39858781 = a;
        double r39858782 = r39858781 * r39858771;
        double r39858783 = r39858780 - r39858782;
        double r39858784 = r39858783 * r39858767;
        double r39858785 = b;
        double r39858786 = r39858779 * r39858770;
        double r39858787 = r39858773 * r39858781;
        double r39858788 = r39858786 - r39858787;
        double r39858789 = r39858785 * r39858788;
        double r39858790 = cbrt(r39858789);
        double r39858791 = r39858790 * r39858790;
        double r39858792 = cbrt(r39858788);
        double r39858793 = cbrt(r39858792);
        double r39858794 = r39858792 * r39858792;
        double r39858795 = r39858794 * r39858785;
        double r39858796 = cbrt(r39858795);
        double r39858797 = r39858793 * r39858796;
        double r39858798 = r39858791 * r39858797;
        double r39858799 = r39858784 - r39858798;
        double r39858800 = r39858778 + r39858799;
        double r39858801 = 2.3221986550473696e-227;
        bool r39858802 = r39858767 <= r39858801;
        double r39858803 = -r39858785;
        double r39858804 = r39858803 * r39858788;
        double r39858805 = r39858804 + r39858778;
        double r39858806 = cbrt(r39858767);
        double r39858807 = r39858806 * r39858806;
        double r39858808 = r39858783 * r39858806;
        double r39858809 = r39858807 * r39858808;
        double r39858810 = r39858809 - r39858789;
        double r39858811 = r39858810 + r39858778;
        double r39858812 = r39858802 ? r39858805 : r39858811;
        double r39858813 = r39858769 ? r39858800 : r39858812;
        return r39858813;
}

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

Original11.3
Target14.9
Herbie11.3
\[\begin{array}{l} \mathbf{if}\;t \lt -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -3.645805544531443e-232

    1. Initial program 10.2

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

    3. Applied add-cube-cbrt10.5

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

    5. Applied add-cube-cbrt10.5

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

    6. Applied associate-*r*10.5

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

    7. Applied cbrt-prod10.5

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

    if -3.645805544531443e-232 < x < 2.3221986550473696e-227

    1. Initial program 16.7

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

    2. Taylor expanded around 0 15.3

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

    if 2.3221986550473696e-227 < x

    1. Initial program 10.1

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

    3. Applied add-cube-cbrt10.4

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

    4. Applied associate-*l*10.4

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

  4. Final simplification11.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.645805544531443 \cdot 10^{-232}:\\ \;\;\;\;\left(c \cdot t - i \cdot y\right) \cdot j + \left(\left(y \cdot z - a \cdot t\right) \cdot x - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \left(\sqrt[3]{\sqrt[3]{z \cdot c - i \cdot a}} \cdot \sqrt[3]{\left(\sqrt[3]{z \cdot c - i \cdot a} \cdot \sqrt[3]{z \cdot c - i \cdot a}\right) \cdot b}\right)\right)\\ \mathbf{elif}\;x \le 2.3221986550473696 \cdot 10^{-227}:\\ \;\;\;\;\left(-b\right) \cdot \left(z \cdot c - i \cdot a\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(y \cdot z - a \cdot t\right) \cdot \sqrt[3]{x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(c \cdot t - i \cdot y\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))))