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

Average Error: 6.3 → 1.2

Time: 32.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -3.366177053613654395798675960966992222011 \cdot 10^{198} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 4.788215598584803852236065219824838534122 \cdot 10^{299}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \left(-\left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r464630 = 2.0;
        double r464631 = x;
        double r464632 = y;
        double r464633 = r464631 * r464632;
        double r464634 = z;
        double r464635 = t;
        double r464636 = r464634 * r464635;
        double r464637 = r464633 + r464636;
        double r464638 = a;
        double r464639 = b;
        double r464640 = c;
        double r464641 = r464639 * r464640;
        double r464642 = r464638 + r464641;
        double r464643 = r464642 * r464640;
        double r464644 = i;
        double r464645 = r464643 * r464644;
        double r464646 = r464637 - r464645;
        double r464647 = r464630 * r464646;
        return r464647;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r464648 = a;
        double r464649 = b;
        double r464650 = c;
        double r464651 = r464649 * r464650;
        double r464652 = r464648 + r464651;
        double r464653 = r464652 * r464650;
        double r464654 = -3.3661770536136544e+198;
        bool r464655 = r464653 <= r464654;
        double r464656 = 4.788215598584804e+299;
        bool r464657 = r464653 <= r464656;
        double r464658 = !r464657;
        bool r464659 = r464655 || r464658;
        double r464660 = 2.0;
        double r464661 = x;
        double r464662 = y;
        double r464663 = r464661 * r464662;
        double r464664 = z;
        double r464665 = t;
        double r464666 = r464664 * r464665;
        double r464667 = r464663 + r464666;
        double r464668 = i;
        double r464669 = r464652 * r464668;
        double r464670 = r464669 * r464650;
        double r464671 = -r464670;
        double r464672 = r464667 + r464671;
        double r464673 = r464660 * r464672;
        double r464674 = r464653 * r464668;
        double r464675 = r464667 - r464674;
        double r464676 = r464660 * r464675;
        double r464677 = r464659 ? r464673 : r464676;
        return r464677;
}

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	6.3
Target	1.7
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 2 regimes

2. if (* (+ a (* b c)) c) < -3.3661770536136544e+198 or 4.788215598584804e+299 < (* (+ a (* b c)) c)

   1. Initial program 41.2

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

   3. Applied sub-neg 41.2

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

   4. Simplified 6.2

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

   6. Applied distribute-rgt-neg-out 6.2

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

   7. Applied distribute-rgt-neg-out 6.2

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

   8. Simplified 6.3

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

   if -3.3661770536136544e+198 < (* (+ a (* b c)) c) < 4.788215598584804e+299

   1. Initial program 0.3

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

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -3.366177053613654395798675960966992222011 \cdot 10^{198} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 4.788215598584803852236065219824838534122 \cdot 10^{299}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \left(-\left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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