Average Error: 11.3 → 5.1
Time: 13.5s
Precision: 64
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -3.414369515820831570610704236356476842558 \cdot 10^{292} \lor \neg \left(b1 \cdot b2 \le -8.920570285255288003225140490033096723389 \cdot 10^{-272} \lor \neg \left(b1 \cdot b2 \le 5.989507253638667303240435404300402458215 \cdot 10^{-222}\right) \land b1 \cdot b2 \le 2.895501126392921286080507373965703281239 \cdot 10^{177}\right):\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{\sqrt[3]{a2} \cdot \sqrt[3]{a2}}}}{\frac{b2}{\sqrt[3]{a2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \end{array}\]
\frac{a1 \cdot a2}{b1 \cdot b2}
↓
\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -3.414369515820831570610704236356476842558 \cdot 10^{292} \lor \neg \left(b1 \cdot b2 \le -8.920570285255288003225140490033096723389 \cdot 10^{-272} \lor \neg \left(b1 \cdot b2 \le 5.989507253638667303240435404300402458215 \cdot 10^{-222}\right) \land b1 \cdot b2 \le 2.895501126392921286080507373965703281239 \cdot 10^{177}\right):\\
\;\;\;\;\frac{\frac{a1}{\frac{b1}{\sqrt[3]{a2} \cdot \sqrt[3]{a2}}}}{\frac{b2}{\sqrt[3]{a2}}}\\

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

\end{array}
double f(double a1, double a2, double b1, double b2) {
        double r71066 = a1;
        double r71067 = a2;
        double r71068 = r71066 * r71067;
        double r71069 = b1;
        double r71070 = b2;
        double r71071 = r71069 * r71070;
        double r71072 = r71068 / r71071;
        return r71072;
}
↓
double f(double a1, double a2, double b1, double b2) {
        double r71073 = b1;
        double r71074 = b2;
        double r71075 = r71073 * r71074;
        double r71076 = -3.4143695158208316e+292;
        bool r71077 = r71075 <= r71076;
        double r71078 = -8.920570285255288e-272;
        bool r71079 = r71075 <= r71078;
        double r71080 = 5.989507253638667e-222;
        bool r71081 = r71075 <= r71080;
        double r71082 = !r71081;
        double r71083 = 2.8955011263929213e+177;
        bool r71084 = r71075 <= r71083;
        bool r71085 = r71082 && r71084;
        bool r71086 = r71079 || r71085;
        double r71087 = !r71086;
        bool r71088 = r71077 || r71087;
        double r71089 = a1;
        double r71090 = a2;
        double r71091 = cbrt(r71090);
        double r71092 = r71091 * r71091;
        double r71093 = r71073 / r71092;
        double r71094 = r71089 / r71093;
        double r71095 = r71074 / r71091;
        double r71096 = r71094 / r71095;
        double r71097 = r71075 / r71090;
        double r71098 = r71089 / r71097;
        double r71099 = r71088 ? r71096 : r71098;
        return r71099;
}

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

Original11.3
Target11.3
Herbie5.1
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 2 regimes

  2. if (* b1 b2) < -3.4143695158208316e+292 or -8.920570285255288e-272 < (* b1 b2) < 5.989507253638667e-222 or 2.8955011263929213e+177 < (* b1 b2)

    1. Initial program 23.6

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

    3. Applied associate-/l*23.8

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

    5. Applied add-cube-cbrt24.0

      \[\leadsto \frac{a1}{\frac{b1 \cdot b2}{\color{blue}{\left(\sqrt[3]{a2} \cdot \sqrt[3]{a2}\right) \cdot \sqrt[3]{a2}}}}\]

    6. Applied times-frac12.2

      \[\leadsto \frac{a1}{\color{blue}{\frac{b1}{\sqrt[3]{a2} \cdot \sqrt[3]{a2}} \cdot \frac{b2}{\sqrt[3]{a2}}}}\]

    7. Applied associate-/r*4.7

      \[\leadsto \color{blue}{\frac{\frac{a1}{\frac{b1}{\sqrt[3]{a2} \cdot \sqrt[3]{a2}}}}{\frac{b2}{\sqrt[3]{a2}}}}\]

    if -3.4143695158208316e+292 < (* b1 b2) < -8.920570285255288e-272 or 5.989507253638667e-222 < (* b1 b2) < 2.8955011263929213e+177

    1. Initial program 5.1

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

    3. Applied associate-/l*5.4

      \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -3.414369515820831570610704236356476842558 \cdot 10^{292} \lor \neg \left(b1 \cdot b2 \le -8.920570285255288003225140490033096723389 \cdot 10^{-272} \lor \neg \left(b1 \cdot b2 \le 5.989507253638667303240435404300402458215 \cdot 10^{-222}\right) \land b1 \cdot b2 \le 2.895501126392921286080507373965703281239 \cdot 10^{177}\right):\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{\sqrt[3]{a2} \cdot \sqrt[3]{a2}}}}{\frac{b2}{\sqrt[3]{a2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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