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

Average Error: 6.2 → 1.7

Time: 18.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r649105 = 2.0;
        double r649106 = x;
        double r649107 = y;
        double r649108 = r649106 * r649107;
        double r649109 = z;
        double r649110 = t;
        double r649111 = r649109 * r649110;
        double r649112 = r649108 + r649111;
        double r649113 = a;
        double r649114 = b;
        double r649115 = c;
        double r649116 = r649114 * r649115;
        double r649117 = r649113 + r649116;
        double r649118 = r649117 * r649115;
        double r649119 = i;
        double r649120 = r649118 * r649119;
        double r649121 = r649112 - r649120;
        double r649122 = r649105 * r649121;
        return r649122;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r649123 = 2.0;
        double r649124 = y;
        double r649125 = x;
        double r649126 = r649124 * r649125;
        double r649127 = z;
        double r649128 = t;
        double r649129 = r649127 * r649128;
        double r649130 = r649126 + r649129;
        double r649131 = a;
        double r649132 = b;
        double r649133 = c;
        double r649134 = r649132 * r649133;
        double r649135 = r649131 + r649134;
        double r649136 = i;
        double r649137 = r649133 * r649136;
        double r649138 = r649135 * r649137;
        double r649139 = r649130 - r649138;
        double r649140 = r649123 * r649139;
        return r649140;
}

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	1.7
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. 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* 1.7

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

4. Simplified 1.7

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

5. Final simplification 1.7

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))