Average Error: 10.8 → 6.7
Time: 11.4s
Precision: 64
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -4.400716313668456 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.4490538368871561 \cdot 10^{-99}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b2}{a2}}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 3.3810800204304724 \cdot 10^{+304}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]
\frac{a1 \cdot a2}{b1 \cdot b2}
↓
\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 = -\infty:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le -4.400716313668456 \cdot 10^{-101}:\\
\;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le 1.4490538368871561 \cdot 10^{-99}:\\
\;\;\;\;\frac{\frac{a1}{\frac{b2}{a2}}}{b1}\\

\mathbf{elif}\;a1 \cdot a2 \le 3.3810800204304724 \cdot 10^{+304}:\\
\;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\

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

\end{array}
double f(double a1, double a2, double b1, double b2) {
        double r2070860 = a1;
        double r2070861 = a2;
        double r2070862 = r2070860 * r2070861;
        double r2070863 = b1;
        double r2070864 = b2;
        double r2070865 = r2070863 * r2070864;
        double r2070866 = r2070862 / r2070865;
        return r2070866;
}
↓
double f(double a1, double a2, double b1, double b2) {
        double r2070867 = a1;
        double r2070868 = a2;
        double r2070869 = r2070867 * r2070868;
        double r2070870 = -inf.0;
        bool r2070871 = r2070869 <= r2070870;
        double r2070872 = b1;
        double r2070873 = r2070867 / r2070872;
        double r2070874 = b2;
        double r2070875 = r2070868 / r2070874;
        double r2070876 = r2070873 * r2070875;
        double r2070877 = -4.400716313668456e-101;
        bool r2070878 = r2070869 <= r2070877;
        double r2070879 = r2070869 / r2070872;
        double r2070880 = r2070879 / r2070874;
        double r2070881 = 1.4490538368871561e-99;
        bool r2070882 = r2070869 <= r2070881;
        double r2070883 = r2070874 / r2070868;
        double r2070884 = r2070867 / r2070883;
        double r2070885 = r2070884 / r2070872;
        double r2070886 = 3.3810800204304724e+304;
        bool r2070887 = r2070869 <= r2070886;
        double r2070888 = r2070887 ? r2070880 : r2070876;
        double r2070889 = r2070882 ? r2070885 : r2070888;
        double r2070890 = r2070878 ? r2070880 : r2070889;
        double r2070891 = r2070871 ? r2070876 : r2070890;
        return r2070891;
}

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

Original10.8
Target11.2
Herbie6.7
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 3 regimes

  2. if (* a1 a2) < -inf.0 or 3.3810800204304724e+304 < (* a1 a2)

    1. Initial program 59.7

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

    3. Applied times-frac8.9

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

    if -inf.0 < (* a1 a2) < -4.400716313668456e-101 or 1.4490538368871561e-99 < (* a1 a2) < 3.3810800204304724e+304

    1. Initial program 5.2

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

    3. Applied associate-/r*5.1

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

    if -4.400716313668456e-101 < (* a1 a2) < 1.4490538368871561e-99

    1. Initial program 11.0

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

    3. Applied associate-/l*8.4

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

    5. Applied *-un-lft-identity8.4

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

    6. Applied times-frac7.1

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

    7. Applied *-un-lft-identity7.1

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

    8. Applied times-frac8.4

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

    9. Simplified8.4

      \[\leadsto \color{blue}{\frac{1}{b1}} \cdot \frac{a1}{\frac{b2}{a2}}\]
    10. Using strategy rm

    11. Applied associate-*l/8.4

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

    12. Simplified8.4

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

  4. Final simplification6.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -4.400716313668456 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.4490538368871561 \cdot 10^{-99}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b2}{a2}}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 3.3810800204304724 \cdot 10^{+304}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019155 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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