Average Error: 11.4 → 2.5
Time: 7.3s
Precision: 64
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -6.6844398141843 \cdot 10^{-312}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 8.55317884451173137 \cdot 10^{276}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]
\frac{a1 \cdot a2}{b1 \cdot b2}
↓
\begin{array}{l}
\mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -6.6844398141843 \cdot 10^{-312}:\\
\;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\

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

\mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 8.55317884451173137 \cdot 10^{276}:\\
\;\;\;\;\frac{a1 \cdot a2}{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 r151224 = a1;
        double r151225 = a2;
        double r151226 = r151224 * r151225;
        double r151227 = b1;
        double r151228 = b2;
        double r151229 = r151227 * r151228;
        double r151230 = r151226 / r151229;
        return r151230;
}
↓
double f(double a1, double a2, double b1, double b2) {
        double r151231 = a1;
        double r151232 = a2;
        double r151233 = r151231 * r151232;
        double r151234 = b1;
        double r151235 = b2;
        double r151236 = r151234 * r151235;
        double r151237 = r151233 / r151236;
        double r151238 = -inf.0;
        bool r151239 = r151237 <= r151238;
        double r151240 = r151231 / r151234;
        double r151241 = r151232 / r151235;
        double r151242 = r151240 * r151241;
        double r151243 = -6.6844398141843e-312;
        bool r151244 = r151237 <= r151243;
        double r151245 = 1.0;
        double r151246 = r151245 / r151234;
        double r151247 = r151246 / r151235;
        double r151248 = r151233 * r151247;
        double r151249 = 0.0;
        bool r151250 = r151237 <= r151249;
        double r151251 = 8.553178844511731e+276;
        bool r151252 = r151237 <= r151251;
        double r151253 = r151252 ? r151237 : r151242;
        double r151254 = r151250 ? r151242 : r151253;
        double r151255 = r151244 ? r151248 : r151254;
        double r151256 = r151239 ? r151242 : r151255;
        return r151256;
}

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
Target11.5
Herbie2.5
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -6.6844398141843e-312 < (/ (* a1 a2) (* b1 b2)) < 0.0 or 8.553178844511731e+276 < (/ (* a1 a2) (* b1 b2))

    1. Initial program 25.7

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

    3. Applied times-frac4.3

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

    if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -6.6844398141843e-312

    1. Initial program 0.9

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

    3. Applied associate-/r*8.9

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

    5. Applied *-un-lft-identity8.9

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

    6. Applied div-inv9.0

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

    7. Applied times-frac1.4

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

    8. Simplified1.4

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

    if 0.0 < (/ (* a1 a2) (* b1 b2)) < 8.553178844511731e+276

    1. Initial program 0.8

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -6.6844398141843 \cdot 10^{-312}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 8.55317884451173137 \cdot 10^{276}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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