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

Average Error: 6.2 → 1.8

Time: 30.7s

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 r38734140 = 2.0;
        double r38734141 = x;
        double r38734142 = y;
        double r38734143 = r38734141 * r38734142;
        double r38734144 = z;
        double r38734145 = t;
        double r38734146 = r38734144 * r38734145;
        double r38734147 = r38734143 + r38734146;
        double r38734148 = a;
        double r38734149 = b;
        double r38734150 = c;
        double r38734151 = r38734149 * r38734150;
        double r38734152 = r38734148 + r38734151;
        double r38734153 = r38734152 * r38734150;
        double r38734154 = i;
        double r38734155 = r38734153 * r38734154;
        double r38734156 = r38734147 - r38734155;
        double r38734157 = r38734140 * r38734156;
        return r38734157;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r38734158 = 2.0;
        double r38734159 = y;
        double r38734160 = x;
        double r38734161 = r38734159 * r38734160;
        double r38734162 = z;
        double r38734163 = t;
        double r38734164 = r38734162 * r38734163;
        double r38734165 = r38734161 + r38734164;
        double r38734166 = a;
        double r38734167 = b;
        double r38734168 = c;
        double r38734169 = r38734167 * r38734168;
        double r38734170 = r38734166 + r38734169;
        double r38734171 = i;
        double r38734172 = r38734168 * r38734171;
        double r38734173 = r38734170 * r38734172;
        double r38734174 = r38734165 - r38734173;
        double r38734175 = r38734158 * r38734174;
        return r38734175;
}

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	1.8
Herbie	1.8

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

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* 1.8

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

4. Final simplification 1.8

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

Reproduce

herbie shell --seed 2019171 
(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))))