Average Error: 11.1 → 5.8
Time: 17.8s
Precision: 64
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -8.129877692652163 \cdot 10^{+206}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.1447059923691223 \cdot 10^{-264}:\\ \;\;\;\;\frac{a2}{b1 \cdot b2} \cdot a1\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.5304753089027245 \cdot 10^{+60}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]
\frac{a1 \cdot a2}{b1 \cdot b2}
↓
\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -8.129877692652163 \cdot 10^{+206}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -1.1447059923691223 \cdot 10^{-264}:\\
\;\;\;\;\frac{a2}{b1 \cdot b2} \cdot a1\\

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

\mathbf{elif}\;b1 \cdot b2 \le 3.5304753089027245 \cdot 10^{+60}:\\
\;\;\;\;\frac{a2 \cdot a1}{b1 \cdot b2}\\

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

\end{array}
double f(double a1, double a2, double b1, double b2) {
        double r4703075 = a1;
        double r4703076 = a2;
        double r4703077 = r4703075 * r4703076;
        double r4703078 = b1;
        double r4703079 = b2;
        double r4703080 = r4703078 * r4703079;
        double r4703081 = r4703077 / r4703080;
        return r4703081;
}
↓
double f(double a1, double a2, double b1, double b2) {
        double r4703082 = b1;
        double r4703083 = b2;
        double r4703084 = r4703082 * r4703083;
        double r4703085 = -8.129877692652163e+206;
        bool r4703086 = r4703084 <= r4703085;
        double r4703087 = a1;
        double r4703088 = r4703087 / r4703082;
        double r4703089 = a2;
        double r4703090 = r4703089 / r4703083;
        double r4703091 = r4703088 * r4703090;
        double r4703092 = -1.1447059923691223e-264;
        bool r4703093 = r4703084 <= r4703092;
        double r4703094 = r4703089 / r4703084;
        double r4703095 = r4703094 * r4703087;
        double r4703096 = -0.0;
        bool r4703097 = r4703084 <= r4703096;
        double r4703098 = 3.5304753089027245e+60;
        bool r4703099 = r4703084 <= r4703098;
        double r4703100 = r4703089 * r4703087;
        double r4703101 = r4703100 / r4703084;
        double r4703102 = r4703099 ? r4703101 : r4703091;
        double r4703103 = r4703097 ? r4703091 : r4703102;
        double r4703104 = r4703093 ? r4703095 : r4703103;
        double r4703105 = r4703086 ? r4703091 : r4703104;
        return r4703105;
}

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
Target11.2
Herbie5.8
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 3 regimes

  2. if (* b1 b2) < -8.129877692652163e+206 or -1.1447059923691223e-264 < (* b1 b2) < -0.0 or 3.5304753089027245e+60 < (* b1 b2)

    1. Initial program 17.7

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

    3. Applied times-frac6.8

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

    if -8.129877692652163e+206 < (* b1 b2) < -1.1447059923691223e-264

    1. Initial program 5.4

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

    3. Applied times-frac14.7

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

    5. Applied div-inv14.8

      \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b1}\right)} \cdot \frac{a2}{b2}\]

    6. Applied associate-*l*11.3

      \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b1} \cdot \frac{a2}{b2}\right)}\]

    7. Simplified4.3

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

    if -0.0 < (* b1 b2) < 3.5304753089027245e+60

    1. Initial program 5.8

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

    3. Applied times-frac15.2

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

    5. Applied div-inv15.3

      \[\leadsto \frac{a1}{b1} \cdot \color{blue}{\left(a2 \cdot \frac{1}{b2}\right)}\]

    6. Applied associate-*r*16.0

      \[\leadsto \color{blue}{\left(\frac{a1}{b1} \cdot a2\right) \cdot \frac{1}{b2}}\]

    7. Taylor expanded around inf 5.8

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

  4. Final simplification5.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -8.129877692652163 \cdot 10^{+206}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.1447059923691223 \cdot 10^{-264}:\\ \;\;\;\;\frac{a2}{b1 \cdot b2} \cdot a1\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.5304753089027245 \cdot 10^{+60}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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