Average Error: 11.7 → 12.0
Time: 11.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{\left(x \cdot \left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
\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)
↓
\left(\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{\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)
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r129642 = x;
        double r129643 = y;
        double r129644 = z;
        double r129645 = r129643 * r129644;
        double r129646 = t;
        double r129647 = a;
        double r129648 = r129646 * r129647;
        double r129649 = r129645 - r129648;
        double r129650 = r129642 * r129649;
        double r129651 = b;
        double r129652 = c;
        double r129653 = r129652 * r129644;
        double r129654 = i;
        double r129655 = r129654 * r129647;
        double r129656 = r129653 - r129655;
        double r129657 = r129651 * r129656;
        double r129658 = r129650 - r129657;
        double r129659 = j;
        double r129660 = r129652 * r129646;
        double r129661 = r129654 * r129643;
        double r129662 = r129660 - r129661;
        double r129663 = r129659 * r129662;
        double r129664 = r129658 + r129663;
        return r129664;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r129665 = x;
        double r129666 = y;
        double r129667 = z;
        double r129668 = r129666 * r129667;
        double r129669 = t;
        double r129670 = a;
        double r129671 = r129669 * r129670;
        double r129672 = r129668 - r129671;
        double r129673 = r129665 * r129672;
        double r129674 = cbrt(r129673);
        double r129675 = r129674 * r129674;
        double r129676 = cbrt(r129672);
        double r129677 = r129676 * r129676;
        double r129678 = r129665 * r129677;
        double r129679 = r129678 * r129676;
        double r129680 = cbrt(r129679);
        double r129681 = r129675 * r129680;
        double r129682 = b;
        double r129683 = c;
        double r129684 = r129683 * r129667;
        double r129685 = i;
        double r129686 = r129685 * r129670;
        double r129687 = r129684 - r129686;
        double r129688 = r129682 * r129687;
        double r129689 = r129681 - r129688;
        double r129690 = j;
        double r129691 = r129683 * r129669;
        double r129692 = r129685 * r129666;
        double r129693 = r129691 - r129692;
        double r129694 = r129690 * r129693;
        double r129695 = r129689 + r129694;
        return r129695;
}

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

Derivation

  1. Initial program 11.7

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

  3. Applied add-cube-cbrt12.0

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

  5. Applied add-cube-cbrt12.0

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

  6. Applied associate-*r*12.0

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

  7. Final simplification12.0

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

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))