Average Error: 6.3 → 1.9
Time: 23.2s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;c \le -3.938516647574964314558470242212887304437 \cdot 10^{107} \lor \neg \left(c \le 2.804777274199547629540334400960615016541 \cdot 10^{-18}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right)\\ \end{array}\]
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}\;c \le -3.938516647574964314558470242212887304437 \cdot 10^{107} \lor \neg \left(c \le 2.804777274199547629540334400960615016541 \cdot 10^{-18}\right):\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r432884 = 2.0;
        double r432885 = x;
        double r432886 = y;
        double r432887 = r432885 * r432886;
        double r432888 = z;
        double r432889 = t;
        double r432890 = r432888 * r432889;
        double r432891 = r432887 + r432890;
        double r432892 = a;
        double r432893 = b;
        double r432894 = c;
        double r432895 = r432893 * r432894;
        double r432896 = r432892 + r432895;
        double r432897 = r432896 * r432894;
        double r432898 = i;
        double r432899 = r432897 * r432898;
        double r432900 = r432891 - r432899;
        double r432901 = r432884 * r432900;
        return r432901;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r432902 = c;
        double r432903 = -3.938516647574964e+107;
        bool r432904 = r432902 <= r432903;
        double r432905 = 2.8047772741995476e-18;
        bool r432906 = r432902 <= r432905;
        double r432907 = !r432906;
        bool r432908 = r432904 || r432907;
        double r432909 = 2.0;
        double r432910 = x;
        double r432911 = y;
        double r432912 = r432910 * r432911;
        double r432913 = z;
        double r432914 = t;
        double r432915 = r432913 * r432914;
        double r432916 = r432912 + r432915;
        double r432917 = a;
        double r432918 = b;
        double r432919 = r432918 * r432902;
        double r432920 = r432917 + r432919;
        double r432921 = i;
        double r432922 = r432920 * r432921;
        double r432923 = r432902 * r432922;
        double r432924 = r432916 - r432923;
        double r432925 = r432909 * r432924;
        double r432926 = r432920 * r432902;
        double r432927 = r432921 * r432926;
        double r432928 = r432916 - r432927;
        double r432929 = r432909 * r432928;
        double r432930 = r432908 ? r432925 : r432929;
        return r432930;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.3
Target1.8
Herbie1.9
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if c < -3.938516647574964e+107 or 2.8047772741995476e-18 < c

    1. Initial program 21.4

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

    3. Applied associate-*l*4.4

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

    4. Simplified4.4

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

    6. Applied associate-*r*3.0

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

    7. Simplified3.0

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

    if -3.938516647574964e+107 < c < 2.8047772741995476e-18

    1. Initial program 1.6

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;c \le -3.938516647574964314558470242212887304437 \cdot 10^{107} \lor \neg \left(c \le 2.804777274199547629540334400960615016541 \cdot 10^{-18}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))