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

Average Error: 6.1 → 1.5

Time: 34.9s

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 r425651 = 2.0;
        double r425652 = x;
        double r425653 = y;
        double r425654 = r425652 * r425653;
        double r425655 = z;
        double r425656 = t;
        double r425657 = r425655 * r425656;
        double r425658 = r425654 + r425657;
        double r425659 = a;
        double r425660 = b;
        double r425661 = c;
        double r425662 = r425660 * r425661;
        double r425663 = r425659 + r425662;
        double r425664 = r425663 * r425661;
        double r425665 = i;
        double r425666 = r425664 * r425665;
        double r425667 = r425658 - r425666;
        double r425668 = r425651 * r425667;
        return r425668;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r425669 = 2.0;
        double r425670 = x;
        double r425671 = y;
        double r425672 = r425670 * r425671;
        double r425673 = z;
        double r425674 = t;
        double r425675 = r425673 * r425674;
        double r425676 = r425672 + r425675;
        double r425677 = a;
        double r425678 = b;
        double r425679 = c;
        double r425680 = r425678 * r425679;
        double r425681 = r425677 + r425680;
        double r425682 = i;
        double r425683 = r425679 * r425682;
        double r425684 = r425681 * r425683;
        double r425685 = r425676 - r425684;
        double r425686 = r425669 * r425685;
        return r425686;
}

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	6.1
Target	1.5
Herbie	1.5

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

Derivation

1. Initial program 6.1

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

3. Applied associate-*l* 1.5

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

4. Final simplification 1.5

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

Reproduce

herbie shell --seed 2019323 
(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))))