Average Error: 11.1 → 5.9
Time: 15.6s
Precision: 64
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -6.937968089239468 \cdot 10^{+243}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -5.331249277666462 \cdot 10^{-146}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.1649363369639183 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.6890648193479676 \cdot 10^{+48}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\ \end{array}\]
\frac{a1 \cdot a2}{b1 \cdot b2}
↓
\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -6.937968089239468 \cdot 10^{+243}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -5.331249277666462 \cdot 10^{-146}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le 2.1649363369639183 \cdot 10^{-186}:\\
\;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 5.6890648193479676 \cdot 10^{+48}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\

\end{array}
double f(double a1, double a2, double b1, double b2) {
        double r7980834 = a1;
        double r7980835 = a2;
        double r7980836 = r7980834 * r7980835;
        double r7980837 = b1;
        double r7980838 = b2;
        double r7980839 = r7980837 * r7980838;
        double r7980840 = r7980836 / r7980839;
        return r7980840;
}
↓
double f(double a1, double a2, double b1, double b2) {
        double r7980841 = b1;
        double r7980842 = b2;
        double r7980843 = r7980841 * r7980842;
        double r7980844 = -6.937968089239468e+243;
        bool r7980845 = r7980843 <= r7980844;
        double r7980846 = a1;
        double r7980847 = r7980846 / r7980841;
        double r7980848 = a2;
        double r7980849 = r7980848 / r7980842;
        double r7980850 = r7980847 * r7980849;
        double r7980851 = -5.331249277666462e-146;
        bool r7980852 = r7980843 <= r7980851;
        double r7980853 = r7980843 / r7980848;
        double r7980854 = r7980846 / r7980853;
        double r7980855 = 2.1649363369639183e-186;
        bool r7980856 = r7980843 <= r7980855;
        double r7980857 = r7980841 / r7980846;
        double r7980858 = r7980848 / r7980857;
        double r7980859 = r7980858 / r7980842;
        double r7980860 = 5.6890648193479676e+48;
        bool r7980861 = r7980843 <= r7980860;
        double r7980862 = r7980861 ? r7980854 : r7980859;
        double r7980863 = r7980856 ? r7980859 : r7980862;
        double r7980864 = r7980852 ? r7980854 : r7980863;
        double r7980865 = r7980845 ? r7980850 : r7980864;
        return r7980865;
}

Error

Bits error versus a1

Bits error versus a2

Bits error versus b1

Bits error versus b2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.1
Target11.4
Herbie5.9
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 3 regimes

  2. if (* b1 b2) < -6.937968089239468e+243

    1. Initial program 18.0

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
    2. Using strategy rm

    3. Applied times-frac3.9

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]

    if -6.937968089239468e+243 < (* b1 b2) < -5.331249277666462e-146 or 2.1649363369639183e-186 < (* b1 b2) < 5.6890648193479676e+48

    1. Initial program 4.1

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
    2. Using strategy rm

    3. Applied associate-/l*3.8

      \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]

    if -5.331249277666462e-146 < (* b1 b2) < 2.1649363369639183e-186 or 5.6890648193479676e+48 < (* b1 b2)

    1. Initial program 17.0

      \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
    2. Using strategy rm

    3. Applied associate-/r*11.8

      \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity11.8

      \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}}\]

    6. Applied associate-/r*11.8

      \[\leadsto \color{blue}{\frac{\frac{\frac{a1 \cdot a2}{b1}}{1}}{b2}}\]

    7. Simplified8.8

      \[\leadsto \frac{\color{blue}{\frac{a2}{\frac{b1}{a1}}}}{b2}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification5.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -6.937968089239468 \cdot 10^{+243}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -5.331249277666462 \cdot 10^{-146}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.1649363369639183 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.6890648193479676 \cdot 10^{+48}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

  :herbie-target
  (* (/ a1 b1) (/ a2 b2))

  (/ (* a1 a2) (* b1 b2)))