Average Error: 12.0 → 9.4
Time: 30.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -36405603859118997733377895825408:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(-x\right) \cdot \left(t \cdot a\right) + \sqrt[3]{x} \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{elif}\;x \le 3.770091383293643248035245981000380783424 \cdot 10^{-95}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + a \cdot \left(t \cdot \left(-x\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt{x} \cdot \left(\left(y \cdot z\right) \cdot \sqrt{x}\right) + \left(-x\right) \cdot \left(t \cdot a\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array}\]
\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}\;x \le -36405603859118997733377895825408:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(-x\right) \cdot \left(t \cdot a\right) + \sqrt[3]{x} \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\

\mathbf{elif}\;x \le 3.770091383293643248035245981000380783424 \cdot 10^{-95}:\\
\;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + a \cdot \left(t \cdot \left(-x\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r28310653 = x;
        double r28310654 = y;
        double r28310655 = z;
        double r28310656 = r28310654 * r28310655;
        double r28310657 = t;
        double r28310658 = a;
        double r28310659 = r28310657 * r28310658;
        double r28310660 = r28310656 - r28310659;
        double r28310661 = r28310653 * r28310660;
        double r28310662 = b;
        double r28310663 = c;
        double r28310664 = r28310663 * r28310655;
        double r28310665 = i;
        double r28310666 = r28310665 * r28310658;
        double r28310667 = r28310664 - r28310666;
        double r28310668 = r28310662 * r28310667;
        double r28310669 = r28310661 - r28310668;
        double r28310670 = j;
        double r28310671 = r28310663 * r28310657;
        double r28310672 = r28310665 * r28310654;
        double r28310673 = r28310671 - r28310672;
        double r28310674 = r28310670 * r28310673;
        double r28310675 = r28310669 + r28310674;
        return r28310675;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r28310676 = x;
        double r28310677 = -3.6405603859118998e+31;
        bool r28310678 = r28310676 <= r28310677;
        double r28310679 = j;
        double r28310680 = t;
        double r28310681 = c;
        double r28310682 = r28310680 * r28310681;
        double r28310683 = y;
        double r28310684 = i;
        double r28310685 = r28310683 * r28310684;
        double r28310686 = r28310682 - r28310685;
        double r28310687 = r28310679 * r28310686;
        double r28310688 = -r28310676;
        double r28310689 = a;
        double r28310690 = r28310680 * r28310689;
        double r28310691 = r28310688 * r28310690;
        double r28310692 = cbrt(r28310676);
        double r28310693 = r28310692 * r28310692;
        double r28310694 = z;
        double r28310695 = r28310683 * r28310694;
        double r28310696 = r28310693 * r28310695;
        double r28310697 = r28310692 * r28310696;
        double r28310698 = r28310691 + r28310697;
        double r28310699 = b;
        double r28310700 = r28310694 * r28310681;
        double r28310701 = r28310684 * r28310689;
        double r28310702 = r28310700 - r28310701;
        double r28310703 = r28310699 * r28310702;
        double r28310704 = r28310698 - r28310703;
        double r28310705 = r28310687 + r28310704;
        double r28310706 = 3.770091383293643e-95;
        bool r28310707 = r28310676 <= r28310706;
        double r28310708 = r28310694 * r28310676;
        double r28310709 = r28310683 * r28310708;
        double r28310710 = r28310680 * r28310688;
        double r28310711 = r28310689 * r28310710;
        double r28310712 = r28310709 + r28310711;
        double r28310713 = r28310712 - r28310703;
        double r28310714 = r28310713 + r28310687;
        double r28310715 = sqrt(r28310676);
        double r28310716 = r28310695 * r28310715;
        double r28310717 = r28310715 * r28310716;
        double r28310718 = r28310717 + r28310691;
        double r28310719 = r28310718 - r28310703;
        double r28310720 = r28310719 + r28310687;
        double r28310721 = r28310707 ? r28310714 : r28310720;
        double r28310722 = r28310678 ? r28310705 : r28310721;
        return r28310722;
}

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

Original12.0
Target15.7
Herbie9.4
\[\begin{array}{l} \mathbf{if}\;t \lt -8.12097891919591218149793027759825150959 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.712553818218485141757938537793350881052 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.633533346031583686060259351057142920433 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.053588855745548710002760210539645467715 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -3.6405603859118998e+31

    1. Initial program 7.2

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

    3. Applied sub-neg7.2

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

    4. Applied distribute-rgt-in7.2

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

    6. Applied add-cube-cbrt7.4

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

    7. Applied associate-*r*7.4

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

    if -3.6405603859118998e+31 < x < 3.770091383293643e-95

    1. Initial program 15.6

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

    3. Applied sub-neg15.6

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

    4. Applied distribute-rgt-in15.6

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

    6. Applied associate-*l*13.1

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

    8. Applied distribute-rgt-neg-in13.1

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

    9. Applied associate-*l*10.5

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

    10. Taylor expanded around inf 10.7

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

    11. Simplified10.7

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

    if 3.770091383293643e-95 < x

    1. Initial program 8.0

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

    3. Applied sub-neg8.0

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

    4. Applied distribute-rgt-in8.0

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

    6. Applied add-sqr-sqrt8.1

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

    7. Applied associate-*r*8.1

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

  4. Final simplification9.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -36405603859118997733377895825408:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(-x\right) \cdot \left(t \cdot a\right) + \sqrt[3]{x} \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{elif}\;x \le 3.770091383293643248035245981000380783424 \cdot 10^{-95}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + a \cdot \left(t \cdot \left(-x\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt{x} \cdot \left(\left(y \cdot z\right) \cdot \sqrt{x}\right) + \left(-x\right) \cdot \left(t \cdot a\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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) 2.0) (pow (* i y) 2.0))) (+ (* 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) 2.0) (pow (* i y) 2.0))) (+ (* 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)))))