Average Error: 11.4 → 5.8
Time: 12.3s
Precision: 64
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.174780128289902610188694526480175085773 \cdot 10^{270}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -8.033401676922496301543611475377383307118 \cdot 10^{-176}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le 1.093710991773609759276773437739228178965 \cdot 10^{120}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \end{array}\]
\frac{a1 \cdot a2}{b1 \cdot b2}
↓
\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -9.174780128289902610188694526480175085773 \cdot 10^{270}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -8.033401676922496301543611475377383307118 \cdot 10^{-176}:\\
\;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\

\mathbf{elif}\;b1 \cdot b2 \le -0.0:\\
\;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\

\mathbf{elif}\;b1 \cdot b2 \le 1.093710991773609759276773437739228178965 \cdot 10^{120}:\\
\;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\

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

\end{array}
double f(double a1, double a2, double b1, double b2) {
        double r6392207 = a1;
        double r6392208 = a2;
        double r6392209 = r6392207 * r6392208;
        double r6392210 = b1;
        double r6392211 = b2;
        double r6392212 = r6392210 * r6392211;
        double r6392213 = r6392209 / r6392212;
        return r6392213;
}
↓
double f(double a1, double a2, double b1, double b2) {
        double r6392214 = b1;
        double r6392215 = b2;
        double r6392216 = r6392214 * r6392215;
        double r6392217 = -9.174780128289903e+270;
        bool r6392218 = r6392216 <= r6392217;
        double r6392219 = a1;
        double r6392220 = r6392219 / r6392214;
        double r6392221 = a2;
        double r6392222 = r6392221 / r6392215;
        double r6392223 = r6392220 * r6392222;
        double r6392224 = -8.033401676922496e-176;
        bool r6392225 = r6392216 <= r6392224;
        double r6392226 = 1.0;
        double r6392227 = r6392221 * r6392219;
        double r6392228 = r6392216 / r6392227;
        double r6392229 = r6392226 / r6392228;
        double r6392230 = -0.0;
        bool r6392231 = r6392216 <= r6392230;
        double r6392232 = r6392221 / r6392214;
        double r6392233 = r6392215 / r6392219;
        double r6392234 = r6392232 / r6392233;
        double r6392235 = 1.0937109917736098e+120;
        bool r6392236 = r6392216 <= r6392235;
        double r6392237 = r6392236 ? r6392229 : r6392234;
        double r6392238 = r6392231 ? r6392234 : r6392237;
        double r6392239 = r6392225 ? r6392229 : r6392238;
        double r6392240 = r6392218 ? r6392223 : r6392239;
        return r6392240;
}

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

Original11.4
Target11.3
Herbie5.8
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 3 regimes

  2. if (* b1 b2) < -9.174780128289903e+270

    1. Initial program 20.3

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

    3. Applied times-frac3.3

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

    if -9.174780128289903e+270 < (* b1 b2) < -8.033401676922496e-176 or -0.0 < (* b1 b2) < 1.0937109917736098e+120

    1. Initial program 4.9

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

    3. Applied clear-num5.3

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

    if -8.033401676922496e-176 < (* b1 b2) < -0.0 or 1.0937109917736098e+120 < (* b1 b2)

    1. Initial program 21.7

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

    3. Applied associate-/r*11.3

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

    5. Applied *-un-lft-identity11.3

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

    6. Applied associate-/r*11.3

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

    7. Simplified7.2

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

    9. Applied associate-/r/7.7

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

    10. Applied associate-/l*7.8

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

  4. Final simplification5.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.174780128289902610188694526480175085773 \cdot 10^{270}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -8.033401676922496301543611475377383307118 \cdot 10^{-176}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le 1.093710991773609759276773437739228178965 \cdot 10^{120}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a2 \cdot a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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