Average Error: 11.1 → 2.5
Time: 34.1s
Precision: 64
Internal Precision: 576
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{a2}{b2}}{b1} \le -9.002484563678713 \cdot 10^{+295}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{if}\;\frac{\frac{a2}{b2}}{b1} \le -7.870597809431541 \cdot 10^{-264}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{if}\;\frac{\frac{a2}{b2}}{b1} \le 5.604703378829582 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{if}\;\frac{\frac{a2}{b2}}{b1} \le 2.2120248113007157 \cdot 10^{+286}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot b2} \cdot a2\\ \end{array}\]

Error

Bits error versus a1

Bits error versus a2

Bits error versus b1

Bits error versus b2

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.1
Target10.9
Herbie2.5
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (/ a2 b2) b1) < -9.002484563678713e+295 or -7.870597809431541e-264 < (/ (/ a2 b2) b1) < 5.604703378829582e-261

    1. Initial program 7.8

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

    3. Applied associate-/r*4.2

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

    if -9.002484563678713e+295 < (/ (/ a2 b2) b1) < -7.870597809431541e-264 or 5.604703378829582e-261 < (/ (/ a2 b2) b1) < 2.2120248113007157e+286

    1. Initial program 12.6

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

    3. Applied associate-/l*6.4

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

    5. Applied associate-/l*0.5

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

    7. Applied clear-num0.6

      \[\leadsto \frac{a1}{\color{blue}{\frac{1}{\frac{\frac{a2}{b2}}{b1}}}}\]
    8. Using strategy rm

    9. Applied div-inv0.5

      \[\leadsto \color{blue}{a1 \cdot \frac{1}{\frac{1}{\frac{\frac{a2}{b2}}{b1}}}}\]

    10. Applied simplify0.5

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

    if 2.2120248113007157e+286 < (/ (/ a2 b2) b1)

    1. Initial program 14.7

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

    3. Applied associate-/l*35.2

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

    5. Applied associate-/r/15.3

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

Runtime

Time bar (total: 34.1s)Debug logProfile

herbie shell --seed 2018198 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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