Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Average Error: 6.4 → 1.2

Time: 2.0m

Precision: 64

Math

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(c \cdot b + a\right) \cdot c\right) \cdot i = -\infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)} \cdot \left(\sqrt[3]{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)} \cdot \left(\sqrt[3]{i \cdot c} \cdot \sqrt[3]{c \cdot b + a}\right)\right)\right)\\ \mathbf{elif}\;\left(\left(c \cdot b + a\right) \cdot c\right) \cdot i \le 2.313994028656579613577693737789861266371 \cdot 10^{292}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \sqrt{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)} \cdot \sqrt{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)}\right) \cdot 2\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r34912745 = 2.0;
        double r34912746 = x;
        double r34912747 = y;
        double r34912748 = r34912746 * r34912747;
        double r34912749 = z;
        double r34912750 = t;
        double r34912751 = r34912749 * r34912750;
        double r34912752 = r34912748 + r34912751;
        double r34912753 = a;
        double r34912754 = b;
        double r34912755 = c;
        double r34912756 = r34912754 * r34912755;
        double r34912757 = r34912753 + r34912756;
        double r34912758 = r34912757 * r34912755;
        double r34912759 = i;
        double r34912760 = r34912758 * r34912759;
        double r34912761 = r34912752 - r34912760;
        double r34912762 = r34912745 * r34912761;
        return r34912762;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r34912763 = c;
        double r34912764 = b;
        double r34912765 = r34912763 * r34912764;
        double r34912766 = a;
        double r34912767 = r34912765 + r34912766;
        double r34912768 = r34912767 * r34912763;
        double r34912769 = i;
        double r34912770 = r34912768 * r34912769;
        double r34912771 = -inf.0;
        bool r34912772 = r34912770 <= r34912771;
        double r34912773 = 2.0;
        double r34912774 = x;
        double r34912775 = y;
        double r34912776 = r34912774 * r34912775;
        double r34912777 = z;
        double r34912778 = t;
        double r34912779 = r34912777 * r34912778;
        double r34912780 = r34912776 + r34912779;
        double r34912781 = r34912769 * r34912763;
        double r34912782 = r34912781 * r34912767;
        double r34912783 = cbrt(r34912782);
        double r34912784 = cbrt(r34912781);
        double r34912785 = cbrt(r34912767);
        double r34912786 = r34912784 * r34912785;
        double r34912787 = r34912783 * r34912786;
        double r34912788 = r34912783 * r34912787;
        double r34912789 = r34912780 - r34912788;
        double r34912790 = r34912773 * r34912789;
        double r34912791 = 2.3139940286565796e+292;
        bool r34912792 = r34912770 <= r34912791;
        double r34912793 = r34912780 - r34912770;
        double r34912794 = r34912793 * r34912773;
        double r34912795 = sqrt(r34912782);
        double r34912796 = r34912795 * r34912795;
        double r34912797 = r34912780 - r34912796;
        double r34912798 = r34912797 * r34912773;
        double r34912799 = r34912792 ? r34912794 : r34912798;
        double r34912800 = r34912772 ? r34912790 : r34912799;
        return r34912800;
}

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

Target

Original	6.4
Target	1.6
Herbie	1.2

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

1. Split input into 3 regimes

2. if (* (* (+ a (* b c)) c) i) < -inf.0

   1. Initial program 64.0

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

   3. Applied associate-*l* 9.5

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]
   4. Using strategy rm

   5. Applied add-cube-cbrt 10.1

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}}\right)\]
   6. Using strategy rm

   7. Applied cbrt-prod 10.0

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \color{blue}{\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{c \cdot i}\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

   if -inf.0 < (* (* (+ a (* b c)) c) i) < 2.3139940286565796e+292

   1. Initial program 0.3

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]

   if 2.3139940286565796e+292 < (* (* (+ a (* b c)) c) i)

   1. Initial program 56.5

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

   3. Applied associate-*l* 8.1

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]
   4. Using strategy rm

   5. Applied add-sqr-sqrt 8.3

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

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(c \cdot b + a\right) \cdot c\right) \cdot i = -\infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)} \cdot \left(\sqrt[3]{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)} \cdot \left(\sqrt[3]{i \cdot c} \cdot \sqrt[3]{c \cdot b + a}\right)\right)\right)\\ \mathbf{elif}\;\left(\left(c \cdot b + a\right) \cdot c\right) \cdot i \le 2.313994028656579613577693737789861266371 \cdot 10^{292}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \sqrt{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)} \cdot \sqrt{\left(i \cdot c\right) \cdot \left(c \cdot b + a\right)}\right) \cdot 2\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))