Average Error: 11.2 → 5.6
Time: 1.8s
Precision: 64
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 = -inf.0 \lor \neg \left(a1 \cdot a2 \le -7.997762846890537 \cdot 10^{-173} \lor \neg \left(a1 \cdot a2 \le 7.0474832780855897 \cdot 10^{-306} \lor \neg \left(a1 \cdot a2 \le 1.57373961865377949 \cdot 10^{151}\right)\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \end{array}\]
\frac{a1 \cdot a2}{b1 \cdot b2}
↓
\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 = -inf.0 \lor \neg \left(a1 \cdot a2 \le -7.997762846890537 \cdot 10^{-173} \lor \neg \left(a1 \cdot a2 \le 7.0474832780855897 \cdot 10^{-306} \lor \neg \left(a1 \cdot a2 \le 1.57373961865377949 \cdot 10^{151}\right)\right)\right):\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

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

\end{array}
double code(double a1, double a2, double b1, double b2) {
	return ((double) (((double) (a1 * a2)) / ((double) (b1 * b2))));
}
↓
double code(double a1, double a2, double b1, double b2) {
	double VAR;
	if (((((double) (a1 * a2)) <= -inf.0) || !((((double) (a1 * a2)) <= -7.997762846890537e-173) || !((((double) (a1 * a2)) <= 7.04748327808559e-306) || !(((double) (a1 * a2)) <= 1.5737396186537795e+151))))) {
		VAR = ((double) (((double) (a1 / b1)) * ((double) (a2 / b2))));
	} else {
		VAR = ((double) (((double) (((double) (a1 * a2)) / b1)) / b2));
	}
	return VAR;
}

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

Original11.2
Target11.4
Herbie5.6
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 2 regimes

  2. if (* a1 a2) < -inf.0 or -7.997762846890537e-173 < (* a1 a2) < 7.04748327808559e-306 or 1.5737396186537795e+151 < (* a1 a2)

    1. Initial program 22.2

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

    3. Applied times-frac6.5

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

    if -inf.0 < (* a1 a2) < -7.997762846890537e-173 or 7.04748327808559e-306 < (* a1 a2) < 1.5737396186537795e+151

    1. Initial program 5.0

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

    3. Applied associate-/r*5.1

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

  4. Final simplification5.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 = -inf.0 \lor \neg \left(a1 \cdot a2 \le -7.997762846890537 \cdot 10^{-173} \lor \neg \left(a1 \cdot a2 \le 7.0474832780855897 \cdot 10^{-306} \lor \neg \left(a1 \cdot a2 \le 1.57373961865377949 \cdot 10^{151}\right)\right)\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2020131 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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