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

Average Error: 6.4 → 1.9

Time: 6.8s

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 r756069 = 2.0;
        double r756070 = x;
        double r756071 = y;
        double r756072 = r756070 * r756071;
        double r756073 = z;
        double r756074 = t;
        double r756075 = r756073 * r756074;
        double r756076 = r756072 + r756075;
        double r756077 = a;
        double r756078 = b;
        double r756079 = c;
        double r756080 = r756078 * r756079;
        double r756081 = r756077 + r756080;
        double r756082 = r756081 * r756079;
        double r756083 = i;
        double r756084 = r756082 * r756083;
        double r756085 = r756076 - r756084;
        double r756086 = r756069 * r756085;
        return r756086;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r756087 = 2.0;
        double r756088 = x;
        double r756089 = y;
        double r756090 = r756088 * r756089;
        double r756091 = z;
        double r756092 = t;
        double r756093 = r756091 * r756092;
        double r756094 = r756090 + r756093;
        double r756095 = a;
        double r756096 = b;
        double r756097 = c;
        double r756098 = r756096 * r756097;
        double r756099 = r756095 + r756098;
        double r756100 = i;
        double r756101 = r756097 * r756100;
        double r756102 = r756099 * r756101;
        double r756103 = r756094 - r756102;
        double r756104 = r756087 * r756103;
        return r756104;
}

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))))