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

Average Error: 6.2 → 1.9

Time: 19.0s

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 r581746 = 2.0;
        double r581747 = x;
        double r581748 = y;
        double r581749 = r581747 * r581748;
        double r581750 = z;
        double r581751 = t;
        double r581752 = r581750 * r581751;
        double r581753 = r581749 + r581752;
        double r581754 = a;
        double r581755 = b;
        double r581756 = c;
        double r581757 = r581755 * r581756;
        double r581758 = r581754 + r581757;
        double r581759 = r581758 * r581756;
        double r581760 = i;
        double r581761 = r581759 * r581760;
        double r581762 = r581753 - r581761;
        double r581763 = r581746 * r581762;
        return r581763;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r581764 = 2.0;
        double r581765 = x;
        double r581766 = y;
        double r581767 = r581765 * r581766;
        double r581768 = z;
        double r581769 = t;
        double r581770 = r581768 * r581769;
        double r581771 = r581767 + r581770;
        double r581772 = a;
        double r581773 = b;
        double r581774 = c;
        double r581775 = r581773 * r581774;
        double r581776 = r581772 + r581775;
        double r581777 = i;
        double r581778 = r581774 * r581777;
        double r581779 = r581776 * r581778;
        double r581780 = r581771 - r581779;
        double r581781 = r581764 * r581780;
        return r581781;
}

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. 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 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))))