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

Average Error: 6.2 → 1.9

Time: 10.8s

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 r731930 = 2.0;
        double r731931 = x;
        double r731932 = y;
        double r731933 = r731931 * r731932;
        double r731934 = z;
        double r731935 = t;
        double r731936 = r731934 * r731935;
        double r731937 = r731933 + r731936;
        double r731938 = a;
        double r731939 = b;
        double r731940 = c;
        double r731941 = r731939 * r731940;
        double r731942 = r731938 + r731941;
        double r731943 = r731942 * r731940;
        double r731944 = i;
        double r731945 = r731943 * r731944;
        double r731946 = r731937 - r731945;
        double r731947 = r731930 * r731946;
        return r731947;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r731948 = 2.0;
        double r731949 = x;
        double r731950 = y;
        double r731951 = r731949 * r731950;
        double r731952 = z;
        double r731953 = t;
        double r731954 = r731952 * r731953;
        double r731955 = r731951 + r731954;
        double r731956 = a;
        double r731957 = b;
        double r731958 = c;
        double r731959 = r731957 * r731958;
        double r731960 = r731956 + r731959;
        double r731961 = i;
        double r731962 = r731958 * r731961;
        double r731963 = r731960 * r731962;
        double r731964 = r731955 - r731963;
        double r731965 = r731948 * r731964;
        return r731965;
}

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. 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 2020036 
(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))))