Average Error: 11.6 → 6.6
Time: 36.2s
Precision: 64
Internal precision: 128
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
⬇
\[\begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -4.333068901791902 \cdot 10^{-282}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -0.0:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 2.451390768683476 \cdot 10^{-38}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Error

Bits error versus a1

Bits error versus a2

Bits error versus b1

Bits error versus b2

Target

Original11.6
Comparison10.8
Herbie6.6
\[ \frac{a1}{b1} \cdot \frac{a2}{b2} \]

Derivation

  1. Split input into 4 regimes.

  2. if (/ (* a1 a2) (* b1 b2)) < -4.333068901791902e-282

    1. Initial program 7.5

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

    3. Applied div-inv 7.9

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

    if -4.333068901791902e-282 < (/ (* a1 a2) (* b1 b2)) < -0.0

    1. Initial program 13.2

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

    3. Applied times-frac 2.8

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

    if -0.0 < (/ (* a1 a2) (* b1 b2)) < 2.451390768683476e-38

    1. Initial program 1.3

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

    3. Applied div-inv 1.4

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

    if 2.451390768683476e-38 < (/ (* a1 a2) (* b1 b2))

    1. Initial program 19.9

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

    3. Applied times-frac 12.9

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
  3. Recombined 4 regimes into one program.
  4. Removed slow pow expressions

Runtime

Time bar (total: 36.2s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1424593044 1042833029 2670409204 2315032527 2843787776 4023920578)'
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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