Error

Derivation

1. Split input into 5 regimes.

2. if re < -1.3055268278777005e+74

   1. Initial program 47.6

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

   2. Applied taylor 0.6

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

   3. Taylor expanded around -inf 0.6

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

   4. Applied simplify 0.6

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

   if -1.3055268278777005e+74 < re < -2.321564696919607e-245

   1. Initial program 19.3

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

   3. Applied add-cube-cbrt 19.3

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

   5. Applied pow3 19.3

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

   6. Applied log-pow 19.4

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

   7. Applied associate-/l* 19.4

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

   if -2.321564696919607e-245 < re < -2.837848394186995e-306

   1. Initial program 32.4

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

   3. Applied add-cube-cbrt 32.4

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

   5. Applied pow3 32.4

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

   6. Applied log-pow 32.4

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

   7. Applied associate-/l* 32.3

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

   8. Applied taylor 0.6

      \[\leadsto \frac{3}{\frac{\log 10}{\log \left(\sqrt[3]{im}\right)}}\]

   9. Taylor expanded around 0 0.6

      \[\leadsto \frac{3}{\frac{\log 10}{\log \left(\sqrt[3]{\color{blue}{im}}\right)}}\]

   if -2.837848394186995e-306 < re < 5.33721959222845e+135

   1. Initial program 21.3

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

   3. Applied add-cube-cbrt 21.3

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

   5. Applied *-un-lft-identity 21.3

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

   6. Applied pow3 21.3

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

   7. Applied log-pow 21.3

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

   8. Applied times-frac 21.3

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

   if 5.33721959222845e+135 < re

   1. Initial program 57.4

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

   2. Applied taylor 0.6

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

   3. Taylor expanded around inf 0.6

      \[\leadsto \frac{\log \color{blue}{re}}{\log 10}\]
3. Recombined 5 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 9.8s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))