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

Average Error: 6.2 → 1.9

Time: 32.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1207914 = 2.0;
        double r1207915 = x;
        double r1207916 = y;
        double r1207917 = r1207915 * r1207916;
        double r1207918 = z;
        double r1207919 = t;
        double r1207920 = r1207918 * r1207919;
        double r1207921 = r1207917 + r1207920;
        double r1207922 = a;
        double r1207923 = b;
        double r1207924 = c;
        double r1207925 = r1207923 * r1207924;
        double r1207926 = r1207922 + r1207925;
        double r1207927 = r1207926 * r1207924;
        double r1207928 = i;
        double r1207929 = r1207927 * r1207928;
        double r1207930 = r1207921 - r1207929;
        double r1207931 = r1207914 * r1207930;
        return r1207931;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1207932 = 2.0;
        double r1207933 = x;
        double r1207934 = y;
        double r1207935 = r1207933 * r1207934;
        double r1207936 = z;
        double r1207937 = t;
        double r1207938 = r1207936 * r1207937;
        double r1207939 = r1207935 + r1207938;
        double r1207940 = a;
        double r1207941 = b;
        double r1207942 = c;
        double r1207943 = r1207941 * r1207942;
        double r1207944 = r1207940 + r1207943;
        double r1207945 = i;
        double r1207946 = r1207945 * r1207942;
        double r1207947 = r1207944 * r1207946;
        double r1207948 = r1207939 - r1207947;
        double r1207949 = r1207932 * r1207948;
        return r1207949;
}

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. Simplified 1.9

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

5. Final simplification 1.9

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

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))))