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

Average Error: 6.5 → 1.7

Time: 9.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le -9.88131 \cdot 10^{-324} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 1.1529310559873625 \cdot 10^{302}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} \cdot \sqrt{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r860889 = 2.0;
        double r860890 = x;
        double r860891 = y;
        double r860892 = r860890 * r860891;
        double r860893 = z;
        double r860894 = t;
        double r860895 = r860893 * r860894;
        double r860896 = r860892 + r860895;
        double r860897 = a;
        double r860898 = b;
        double r860899 = c;
        double r860900 = r860898 * r860899;
        double r860901 = r860897 + r860900;
        double r860902 = r860901 * r860899;
        double r860903 = i;
        double r860904 = r860902 * r860903;
        double r860905 = r860896 - r860904;
        double r860906 = r860889 * r860905;
        return r860906;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r860907 = a;
        double r860908 = b;
        double r860909 = c;
        double r860910 = r860908 * r860909;
        double r860911 = r860907 + r860910;
        double r860912 = r860911 * r860909;
        double r860913 = i;
        double r860914 = r860912 * r860913;
        double r860915 = -9.8813129168249e-324;
        bool r860916 = r860914 <= r860915;
        double r860917 = 1.1529310559873625e+302;
        bool r860918 = r860914 <= r860917;
        double r860919 = !r860918;
        bool r860920 = r860916 || r860919;
        double r860921 = 2.0;
        double r860922 = x;
        double r860923 = y;
        double r860924 = r860922 * r860923;
        double r860925 = z;
        double r860926 = t;
        double r860927 = r860925 * r860926;
        double r860928 = r860924 + r860927;
        double r860929 = r860909 * r860913;
        double r860930 = r860911 * r860929;
        double r860931 = r860928 - r860930;
        double r860932 = r860921 * r860931;
        double r860933 = sqrt(r860914);
        double r860934 = r860933 * r860933;
        double r860935 = r860928 - r860934;
        double r860936 = r860921 * r860935;
        double r860937 = r860920 ? r860932 : r860936;
        return r860937;
}

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	6.5
Target	1.9
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. Split input into 2 regimes

2. if (* (* (+ a (* b c)) c) i) < -9.8813129168249e-324 or 1.1529310559873625e+302 < (* (* (+ a (* b c)) c) i)

   1. Initial program 13.8

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

   3. Applied associate-*l* 3.2

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

   if -9.8813129168249e-324 < (* (* (+ a (* b c)) c) i) < 1.1529310559873625e+302

   1. Initial program 0.4

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

   3. Applied add-sqr-sqrt 0.5

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\sqrt{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} \cdot \sqrt{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}}\right)\]
3. Recombined 2 regimes into one program.

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le -9.88131 \cdot 10^{-324} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 1.1529310559873625 \cdot 10^{302}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} \cdot \sqrt{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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))))