Error

Derivation

1. Split input into 5 regimes.

2. if im < -2.809105747846623e+30

   1. Initial program 44.3

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

   2. Applied simplify 44.3

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

   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 -2.809105747846623e+30 < im < -2.6177813920228387e-236

   1. Initial program 19.3

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

   2. Applied simplify 19.3

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

   4. Applied add-cbrt-cube 19.9

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

   5. Applied add-cbrt-cube 19.8

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

   6. Applied cbrt-undiv 19.4

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

   7. Applied simplify 19.4

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

   if -2.6177813920228387e-236 < im < 6.202292738103542e-168

   1. Initial program 29.9

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

   2. Applied simplify 29.9

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

   4. Applied clear-num 29.9

      \[\leadsto \color{blue}{\frac{1}{\frac{\log 10}{\log \left(\sqrt{{im}^2 + re \cdot re}\right)}}}\]
   5. Using strategy rm

   6. Applied add-cbrt-cube 30.0

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

   7. Applied add-cbrt-cube 30.3

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

   8. Applied cbrt-undiv 30.0

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

   9. Applied simplify 30.0

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

   10. Applied taylor 0.7

       \[\leadsto \frac{1}{\sqrt[3]{{\left(\frac{\log 10}{\log \left(-1 \cdot re\right)}\right)}^3}}\]

   11. Taylor expanded around -inf 0.7

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

   12. Applied simplify 0.6

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

   if 6.202292738103542e-168 < im < 1.5950010569398068e+130

   1. Initial program 15.4

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

   2. Applied simplify 15.4

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

   4. Applied clear-num 15.4

      \[\leadsto \color{blue}{\frac{1}{\frac{\log 10}{\log \left(\sqrt{{im}^2 + re \cdot re}\right)}}}\]
   5. Using strategy rm

   6. Applied add-cbrt-cube 15.5

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

   7. Applied add-cbrt-cube 15.9

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

   8. Applied cbrt-undiv 15.4

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

   9. Applied simplify 15.5

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

   if 1.5950010569398068e+130 < im

   1. Initial program 56.2

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

   2. Applied simplify 56.2

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

   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 5 regimes into one program.
4. Removed slow pow expressions

Runtime

Total time: 40.7s Debug log

Please include this information when filing a bug report:

herbie --seed '#(3642402179 2388761754 3684707313 2191577141 461247401 4148109162)'
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))