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

Average Error: 6.2 → 1.9

Time: 33.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1168722 = 2.0;
        double r1168723 = x;
        double r1168724 = y;
        double r1168725 = r1168723 * r1168724;
        double r1168726 = z;
        double r1168727 = t;
        double r1168728 = r1168726 * r1168727;
        double r1168729 = r1168725 + r1168728;
        double r1168730 = a;
        double r1168731 = b;
        double r1168732 = c;
        double r1168733 = r1168731 * r1168732;
        double r1168734 = r1168730 + r1168733;
        double r1168735 = r1168734 * r1168732;
        double r1168736 = i;
        double r1168737 = r1168735 * r1168736;
        double r1168738 = r1168729 - r1168737;
        double r1168739 = r1168722 * r1168738;
        return r1168739;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1168740 = 2.0;
        double r1168741 = x;
        double r1168742 = y;
        double r1168743 = r1168741 * r1168742;
        double r1168744 = z;
        double r1168745 = t;
        double r1168746 = r1168744 * r1168745;
        double r1168747 = r1168743 + r1168746;
        double r1168748 = a;
        double r1168749 = b;
        double r1168750 = c;
        double r1168751 = r1168749 * r1168750;
        double r1168752 = r1168748 + r1168751;
        double r1168753 = i;
        double r1168754 = r1168753 * r1168750;
        double r1168755 = r1168752 * r1168754;
        double r1168756 = r1168747 - r1168755;
        double r1168757 = r1168740 * r1168756;
        return r1168757;
}

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	6.2
Target	1.9
Herbie	1.9

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

Derivation

1. Initial program 6.2

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

3. Applied associate-*l* 1.9

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

4. Simplified 1.9

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

5. Final simplification 1.9

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

Reproduce

herbie shell --seed 2019303 
(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))))