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

Average Error: 6.3 → 1.3

Time: 36.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c = -\infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;\left(a + b \cdot c\right) \cdot c \le 1.710439370453902556184508528678794041422 \cdot 10^{305}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \left(-i\right) \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r472864 = 2.0;
        double r472865 = x;
        double r472866 = y;
        double r472867 = r472865 * r472866;
        double r472868 = z;
        double r472869 = t;
        double r472870 = r472868 * r472869;
        double r472871 = r472867 + r472870;
        double r472872 = a;
        double r472873 = b;
        double r472874 = c;
        double r472875 = r472873 * r472874;
        double r472876 = r472872 + r472875;
        double r472877 = r472876 * r472874;
        double r472878 = i;
        double r472879 = r472877 * r472878;
        double r472880 = r472871 - r472879;
        double r472881 = r472864 * r472880;
        return r472881;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r472882 = a;
        double r472883 = b;
        double r472884 = c;
        double r472885 = r472883 * r472884;
        double r472886 = r472882 + r472885;
        double r472887 = r472886 * r472884;
        double r472888 = -inf.0;
        bool r472889 = r472887 <= r472888;
        double r472890 = 2.0;
        double r472891 = x;
        double r472892 = y;
        double r472893 = r472891 * r472892;
        double r472894 = z;
        double r472895 = t;
        double r472896 = r472894 * r472895;
        double r472897 = r472893 + r472896;
        double r472898 = cbrt(r472886);
        double r472899 = r472898 * r472898;
        double r472900 = r472899 * r472898;
        double r472901 = i;
        double r472902 = r472884 * r472901;
        double r472903 = r472900 * r472902;
        double r472904 = r472897 - r472903;
        double r472905 = r472890 * r472904;
        double r472906 = 1.7104393704539026e+305;
        bool r472907 = r472887 <= r472906;
        double r472908 = -r472901;
        double r472909 = r472908 * r472887;
        double r472910 = r472897 + r472909;
        double r472911 = r472890 * r472910;
        double r472912 = r472886 * r472902;
        double r472913 = cbrt(r472912);
        double r472914 = r472913 * r472913;
        double r472915 = r472914 * r472913;
        double r472916 = r472897 - r472915;
        double r472917 = r472890 * r472916;
        double r472918 = r472907 ? r472911 : r472917;
        double r472919 = r472889 ? r472905 : r472918;
        return r472919;
}

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	6.3
Target	1.8
Herbie	1.3

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

Derivation

1. Split input into 3 regimes

2. if (* (+ a (* b c)) c) < -inf.0

   1. Initial program 64.0

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

   3. Applied associate-*l* 10.6

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

   5. Applied add-cube-cbrt 11.2

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

   if -inf.0 < (* (+ a (* b c)) c) < 1.7104393704539026e+305

   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 associate-*l* 1.0

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

   5. Applied sub-neg 1.0

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

   6. Simplified 0.4

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

   if 1.7104393704539026e+305 < (* (+ a (* b c)) c)

   1. Initial program 63.0

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

   3. Applied associate-*l* 9.5

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

   5. Applied add-cube-cbrt 10.1

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c = -\infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;\left(a + b \cdot c\right) \cdot c \le 1.710439370453902556184508528678794041422 \cdot 10^{305}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \left(-i\right) \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(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))))