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

Average Error: 6.4 → 1.9

Time: 6.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r735710 = 2.0;
        double r735711 = x;
        double r735712 = y;
        double r735713 = r735711 * r735712;
        double r735714 = z;
        double r735715 = t;
        double r735716 = r735714 * r735715;
        double r735717 = r735713 + r735716;
        double r735718 = a;
        double r735719 = b;
        double r735720 = c;
        double r735721 = r735719 * r735720;
        double r735722 = r735718 + r735721;
        double r735723 = r735722 * r735720;
        double r735724 = i;
        double r735725 = r735723 * r735724;
        double r735726 = r735717 - r735725;
        double r735727 = r735710 * r735726;
        return r735727;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r735728 = 2.0;
        double r735729 = x;
        double r735730 = y;
        double r735731 = r735729 * r735730;
        double r735732 = z;
        double r735733 = t;
        double r735734 = r735732 * r735733;
        double r735735 = r735731 + r735734;
        double r735736 = a;
        double r735737 = b;
        double r735738 = c;
        double r735739 = r735737 * r735738;
        double r735740 = r735736 + r735739;
        double r735741 = i;
        double r735742 = r735738 * r735741;
        double r735743 = r735740 * r735742;
        double r735744 = r735735 - r735743;
        double r735745 = r735728 * r735744;
        return r735745;
}

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	1.9
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 6.4

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

3. Applied associate-*l* 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. Final simplification 1.9

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

Reproduce

herbie shell --seed 2020001 
(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))))