Average Error: 10.5 → 3.0
Time: 43.8s
Precision: 64
Internal Precision: 576
\[\frac{a1 \cdot a2}{b1 \cdot b2}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}} \cdot \sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \left(\sqrt[3]{\frac{a1}{b1}} \cdot \frac{a2}{b2}\right)} \le -1.0704377314425847 \cdot 10^{+304}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{if}\;\left(\sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}} \cdot \sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \left(\sqrt[3]{\frac{a1}{b1}} \cdot \frac{a2}{b2}\right)} \le -6.1980387051091 \cdot 10^{-318}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;\left(\sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}} \cdot \sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \left(\sqrt[3]{\frac{a1}{b1}} \cdot \frac{a2}{b2}\right)} \le 2.5475085141972532 \cdot 10^{-297}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{if}\;\left(\sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}} \cdot \sqrt[3]{\frac{a1}{b1} \cdot \frac{a2}{b2}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \left(\sqrt[3]{\frac{a1}{b1}} \cdot \frac{a2}{b2}\right)} \le 4.0521763659347775 \cdot 10^{+294}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \end{array}\]

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

Original10.5
Target10.3
Herbie3.0
\[\frac{a1}{b1} \cdot \frac{a2}{b2}\]

Derivation

  1. Split input into 4 regimes

  2. if (* (* (cbrt (* (/ a1 b1) (/ a2 b2))) (cbrt (* (/ a1 b1) (/ a2 b2)))) (cbrt (* (* (cbrt (/ a1 b1)) (cbrt (/ a1 b1))) (* (cbrt (/ a1 b1)) (/ a2 b2))))) < -1.0704377314425847e+304

    1. Initial program 9.9

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

    if -1.0704377314425847e+304 < (* (* (cbrt (* (/ a1 b1) (/ a2 b2))) (cbrt (* (/ a1 b1) (/ a2 b2)))) (cbrt (* (* (cbrt (/ a1 b1)) (cbrt (/ a1 b1))) (* (cbrt (/ a1 b1)) (/ a2 b2))))) < -6.1980387051091e-318 or 2.5475085141972532e-297 < (* (* (cbrt (* (/ a1 b1) (/ a2 b2))) (cbrt (* (/ a1 b1) (/ a2 b2)))) (cbrt (* (* (cbrt (/ a1 b1)) (cbrt (/ a1 b1))) (* (cbrt (/ a1 b1)) (/ a2 b2))))) < 4.0521763659347775e+294

    1. Initial program 15.5

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

    3. Applied times-frac0.9

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

    if -6.1980387051091e-318 < (* (* (cbrt (* (/ a1 b1) (/ a2 b2))) (cbrt (* (/ a1 b1) (/ a2 b2)))) (cbrt (* (* (cbrt (/ a1 b1)) (cbrt (/ a1 b1))) (* (cbrt (/ a1 b1)) (/ a2 b2))))) < 2.5475085141972532e-297

    1. Initial program 2.4

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

    3. Applied associate-/l*3.8

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

    if 4.0521763659347775e+294 < (* (* (cbrt (* (/ a1 b1) (/ a2 b2))) (cbrt (* (/ a1 b1) (/ a2 b2)))) (cbrt (* (* (cbrt (/ a1 b1)) (cbrt (/ a1 b1))) (* (cbrt (/ a1 b1)) (/ a2 b2)))))

    1. Initial program 6.0

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

    3. Applied associate-/r*14.0

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

Runtime

Time bar (total: 43.8s)Debug logProfile

herbie shell --seed 2018296 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"

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

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