Error

Derivation

1. Split input into 3 regimes.

2. if im < -3.1392156119995164e+40

   1. Initial program 45.8

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]

   2. Applied simplify 45.8

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{{im}^2 + re \cdot re}\right)}{\log 10}}\]

   3. Applied taylor 0.6

      \[\leadsto \frac{\log \left(-1 \cdot im\right)}{\log 10}\]

   4. Taylor expanded around -inf 0.6

      \[\leadsto \frac{\log \color{blue}{\left(-1 \cdot im\right)}}{\log 10}\]

   5. Applied simplify 0.6

      \[\leadsto \color{blue}{\frac{\log \left(-im\right)}{\log 10}}\]

   if -3.1392156119995164e+40 < im < 5.8170505962259145e+31

   1. Initial program 22.3

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]

   2. Applied simplify 22.3

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{{im}^2 + re \cdot re}\right)}{\log 10}}\]
   3. Using strategy rm

   4. Applied add-cube-cbrt 22.3

      \[\leadsto \frac{\log \color{blue}{\left({\left(\sqrt[3]{\sqrt{{im}^2 + re \cdot re}}\right)}^3\right)}}{\log 10}\]
   5. Using strategy rm

   6. Applied pow3 22.3

      \[\leadsto \frac{\log \color{blue}{\left({\left(\sqrt[3]{\sqrt{{im}^2 + re \cdot re}}\right)}^{3}\right)}}{\log 10}\]

   7. Applied log-pow 22.3

      \[\leadsto \frac{\color{blue}{3 \cdot \log \left(\sqrt[3]{\sqrt{{im}^2 + re \cdot re}}\right)}}{\log 10}\]

   8. Applied associate-/l* 22.3

      \[\leadsto \color{blue}{\frac{3}{\frac{\log 10}{\log \left(\sqrt[3]{\sqrt{{im}^2 + re \cdot re}}\right)}}}\]
   9. Using strategy rm

   10. Applied div-inv 22.3

       \[\leadsto \frac{3}{\color{blue}{\log 10 \cdot \frac{1}{\log \left(\sqrt[3]{\sqrt{{im}^2 + re \cdot re}}\right)}}}\]

   if 5.8170505962259145e+31 < im

   1. Initial program 42.7

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]

   2. Applied simplify 42.7

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{{im}^2 + re \cdot re}\right)}{\log 10}}\]

   3. Applied taylor 0.6

      \[\leadsto \frac{\log im}{\log 10}\]

   4. Taylor expanded around inf 0.6

      \[\leadsto \frac{\log \color{blue}{im}}{\log 10}\]
3. Recombined 3 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 22.9s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(283823130 3901138988 2672121530 4088188533 769191305 236709709)'
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))