Quotient of products

Average Error: 11.1 → 2.3

Time: 9.2s

Precision: 64

Math

\[\frac{a1 \cdot a2}{b1 \cdot b2}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \le -3.721065323848875903560093256362069823088 \cdot 10^{-309} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \le 8.682799991236733148187736602059382241979 \cdot 10^{294}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \end{array}\]

C

double f(double a1, double a2, double b1, double b2) {
        double r132731 = a1;
        double r132732 = a2;
        double r132733 = r132731 * r132732;
        double r132734 = b1;
        double r132735 = b2;
        double r132736 = r132734 * r132735;
        double r132737 = r132733 / r132736;
        return r132737;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r132738 = a1;
        double r132739 = a2;
        double r132740 = r132738 * r132739;
        double r132741 = b1;
        double r132742 = b2;
        double r132743 = r132741 * r132742;
        double r132744 = r132740 / r132743;
        double r132745 = -inf.0;
        bool r132746 = r132744 <= r132745;
        double r132747 = -3.721065323848876e-309;
        bool r132748 = r132744 <= r132747;
        double r132749 = 0.0;
        bool r132750 = r132744 <= r132749;
        double r132751 = !r132750;
        double r132752 = 8.682799991236733e+294;
        bool r132753 = r132744 <= r132752;
        bool r132754 = r132751 && r132753;
        bool r132755 = r132748 || r132754;
        double r132756 = !r132755;
        bool r132757 = r132746 || r132756;
        double r132758 = r132738 / r132741;
        double r132759 = r132739 / r132742;
        double r132760 = r132758 * r132759;
        double r132761 = r132757 ? r132760 : r132744;
        return r132761;
}

Error

Bits error versus a1

Bits error versus a2

Bits error versus b1

Bits error versus b2

Target

Original	11.1
Target	11.7
Herbie	2.3

\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

1. Split input into 2 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -3.721065323848876e-309 < (/ (* a1 a2) (* b1 b2)) < 0.0 or 8.682799991236733e+294 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 32.8

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

   3. Applied times-frac 5.6

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -3.721065323848876e-309 or 0.0 < (/ (* a1 a2) (* b1 b2)) < 8.682799991236733e+294

   1. Initial program 3.5

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

4. Final simplification 2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} = -\infty \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \le -3.721065323848875903560093256362069823088 \cdot 10^{-309} \lor \neg \left(\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0\right) \land \frac{a1 \cdot a2}{b1 \cdot b2} \le 8.682799991236733148187736602059382241979 \cdot 10^{294}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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