Error

Try it out

Derivation

1. Split input into 4 regimes

2. if re < -5.313865136797356e+146

   1. Initial program 57.0

      \[\sqrt{re \cdot re + im \cdot im}\]

   2. Initial simplification57.0

      \[\leadsto \sqrt{re \cdot re + im \cdot im}\]

   3. Taylor expanded around -inf 8.2

      \[\leadsto \color{blue}{-1 \cdot re}\]

   4. Simplified8.2

      \[\leadsto \color{blue}{-re}\]

   if -5.313865136797356e+146 < re < 2.273780908986114e-292 or 1.4029821953931988e-209 < re < 1.317497755195432e+154

   1. Initial program 18.3

      \[\sqrt{re \cdot re + im \cdot im}\]

   2. Initial simplification18.3

      \[\leadsto \sqrt{re \cdot re + im \cdot im}\]

   if 2.273780908986114e-292 < re < 1.4029821953931988e-209

   1. Initial program 29.9

      \[\sqrt{re \cdot re + im \cdot im}\]

   2. Initial simplification29.9

      \[\leadsto \sqrt{re \cdot re + im \cdot im}\]

   3. Taylor expanded around 0 36.4

      \[\leadsto \color{blue}{im}\]

   if 1.317497755195432e+154 < re

   1. Initial program 59.4

      \[\sqrt{re \cdot re + im \cdot im}\]

   2. Initial simplification59.4

      \[\leadsto \sqrt{re \cdot re + im \cdot im}\]

   3. Taylor expanded around inf 7.4

      \[\leadsto \color{blue}{re}\]
3. Recombined 4 regimes into one program.

4. Final simplification16.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -5.313865136797356 \cdot 10^{+146}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.273780908986114 \cdot 10^{-292}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{elif}\;re \le 1.4029821953931988 \cdot 10^{-209}:\\ \;\;\;\;im\\ \mathbf{elif}\;re \le 1.317497755195432 \cdot 10^{+154}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Runtime

Time bar (total: 3.9s)Debug logProfile

herbie shell --seed 2018349 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))