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

Average Error: 6.5 → 1.7

Time: 7.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i = -\infty \lor \neg \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 2.2435647671729576 \cdot 10^{-66}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r617753 = 2.0;
        double r617754 = x;
        double r617755 = y;
        double r617756 = r617754 * r617755;
        double r617757 = z;
        double r617758 = t;
        double r617759 = r617757 * r617758;
        double r617760 = r617756 + r617759;
        double r617761 = a;
        double r617762 = b;
        double r617763 = c;
        double r617764 = r617762 * r617763;
        double r617765 = r617761 + r617764;
        double r617766 = r617765 * r617763;
        double r617767 = i;
        double r617768 = r617766 * r617767;
        double r617769 = r617760 - r617768;
        double r617770 = r617753 * r617769;
        return r617770;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r617771 = x;
        double r617772 = y;
        double r617773 = r617771 * r617772;
        double r617774 = z;
        double r617775 = t;
        double r617776 = r617774 * r617775;
        double r617777 = r617773 + r617776;
        double r617778 = a;
        double r617779 = b;
        double r617780 = c;
        double r617781 = r617779 * r617780;
        double r617782 = r617778 + r617781;
        double r617783 = r617782 * r617780;
        double r617784 = i;
        double r617785 = r617783 * r617784;
        double r617786 = r617777 - r617785;
        double r617787 = -inf.0;
        bool r617788 = r617786 <= r617787;
        double r617789 = 2.2435647671729576e-66;
        bool r617790 = r617786 <= r617789;
        double r617791 = !r617790;
        bool r617792 = r617788 || r617791;
        double r617793 = 2.0;
        double r617794 = r617780 * r617784;
        double r617795 = r617782 * r617794;
        double r617796 = r617777 - r617795;
        double r617797 = r617793 * r617796;
        double r617798 = r617793 * r617786;
        double r617799 = r617792 ? r617797 : r617798;
        return r617799;
}

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	6.5
Target	1.9
Herbie	1.7

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

Derivation

1. Split input into 2 regimes

2. if (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i)) < -inf.0 or 2.2435647671729576e-66 < (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))

   1. Initial program 12.4

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

   3. Applied associate-*l* 2.8

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

   if -inf.0 < (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i)) < 2.2435647671729576e-66

   1. Initial program 0.5

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

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i = -\infty \lor \neg \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 2.2435647671729576 \cdot 10^{-66}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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))))