Quotient of products

Average Error: 11.1 → 11.1

Time: 4.9s

Precision: 64

Math

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

↓

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

C

double f(double a1, double a2, double b1, double b2) {
        double r90161 = a1;
        double r90162 = a2;
        double r90163 = r90161 * r90162;
        double r90164 = b1;
        double r90165 = b2;
        double r90166 = r90164 * r90165;
        double r90167 = r90163 / r90166;
        return r90167;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r90168 = a1;
        double r90169 = a2;
        double r90170 = r90168 * r90169;
        double r90171 = b1;
        double r90172 = b2;
        double r90173 = r90171 * r90172;
        double r90174 = r90170 / r90173;
        return r90174;
}

Error

Bits error versus a1

Bits error versus a2

Bits error versus b1

Bits error versus b2

Target

Original	11.1
Target	11.3
Herbie	11.1

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

Derivation

1. Split input into 2 regimes

2. if (/ (* a1 a2) (* b1 b2)) < -inf.0 or -8.150496738080393e-304 < (/ (* a1 a2) (* b1 b2)) < 0.0 or 1.1733062016682887e+275 < (/ (* a1 a2) (* b1 b2))

   1. Initial program 31.0

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

   3. Applied times-frac 5.5

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

   if -inf.0 < (/ (* a1 a2) (* b1 b2)) < -8.150496738080393e-304 or 0.0 < (/ (* a1 a2) (* b1 b2)) < 1.1733062016682887e+275

   1. Initial program 3.5

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

4. Final simplification 11.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

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

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