Average Error: 12.0 → 12.3
Time: 8.5s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right)\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}\]
\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(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(j \cdot \left(\sqrt[3]{c \cdot t - i \cdot y} \cdot \sqrt[3]{c \cdot t - i \cdot y}\right)\right) \cdot \sqrt[3]{c \cdot t - i \cdot y}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r110600 = x;
        double r110601 = y;
        double r110602 = z;
        double r110603 = r110601 * r110602;
        double r110604 = t;
        double r110605 = a;
        double r110606 = r110604 * r110605;
        double r110607 = r110603 - r110606;
        double r110608 = r110600 * r110607;
        double r110609 = b;
        double r110610 = c;
        double r110611 = r110610 * r110602;
        double r110612 = i;
        double r110613 = r110612 * r110605;
        double r110614 = r110611 - r110613;
        double r110615 = r110609 * r110614;
        double r110616 = r110608 - r110615;
        double r110617 = j;
        double r110618 = r110610 * r110604;
        double r110619 = r110612 * r110601;
        double r110620 = r110618 - r110619;
        double r110621 = r110617 * r110620;
        double r110622 = r110616 + r110621;
        return r110622;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r110623 = x;
        double r110624 = y;
        double r110625 = z;
        double r110626 = r110624 * r110625;
        double r110627 = t;
        double r110628 = a;
        double r110629 = r110627 * r110628;
        double r110630 = r110626 - r110629;
        double r110631 = r110623 * r110630;
        double r110632 = b;
        double r110633 = c;
        double r110634 = r110633 * r110625;
        double r110635 = i;
        double r110636 = r110635 * r110628;
        double r110637 = r110634 - r110636;
        double r110638 = r110632 * r110637;
        double r110639 = r110631 - r110638;
        double r110640 = j;
        double r110641 = r110633 * r110627;
        double r110642 = r110635 * r110624;
        double r110643 = r110641 - r110642;
        double r110644 = cbrt(r110643);
        double r110645 = r110644 * r110644;
        double r110646 = r110640 * r110645;
        double r110647 = r110646 * r110644;
        double r110648 = r110639 + r110647;
        return r110648;
}

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 12.0

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

  3. Applied add-cube-cbrt12.3

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

  4. Applied associate-*r*12.3

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

  5. Final simplification12.3

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

Reproduce

herbie shell --seed 2020027 
(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)))))