Average Error: 11.2 → 2.5
Time: 42.1s
Precision: 64
Internal Precision: 384
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{a1}{b1} \cdot \frac{a2}{b2} = -\infty:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \mathbf{if}\;\frac{a1}{b1} \cdot \frac{a2}{b2} \le -6.1104555447917 \cdot 10^{-315}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;\frac{a1}{b1} \cdot \frac{a2}{b2} \le 1.2496181882040065 \cdot 10^{-305}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \mathbf{if}\;\frac{a1}{b1} \cdot \frac{a2}{b2} \le 5.4538264489329024 \cdot 10^{+302}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \end{array}\]

Error

Bits error versus a1

Bits error versus a2

Bits error versus b1

Bits error versus b2

Target

Original11.2
Target11.3
Herbie2.5
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (/ a1 b1) (/ a2 b2)) < -inf.0

    1. Initial program 8.9

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

    3. Applied associate-/r*15.1

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

    5. Applied associate-/l*14.3

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

    if -inf.0 < (* (/ a1 b1) (/ a2 b2)) < -6.1104555447917e-315 or 1.2496181882040065e-305 < (* (/ a1 b1) (/ a2 b2)) < 5.4538264489329024e+302

    1. Initial program 16.7

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

    3. Applied times-frac0.8

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

    if -6.1104555447917e-315 < (* (/ a1 b1) (/ a2 b2)) < 1.2496181882040065e-305 or 5.4538264489329024e+302 < (* (/ a1 b1) (/ a2 b2))

    1. Initial program 3.3

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

    3. Applied clear-num3.7

      \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
  3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 42.1s)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' +o rules:numerics
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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