Error

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Derivation

1. Split input into 4 regimes

2. if re < -1.758999353527392e+183

   1. Initial program 59.1

      \[\sqrt{re \cdot re + im \cdot im}\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt59.1

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

   4. Applied sqrt-prod59.1

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

   5. Taylor expanded around -inf 7.0

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

   6. Simplified7.0

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

   if -1.758999353527392e+183 < re < -1.7987418643598683e-280 or 2.4967545228125466e-154 < re < 1.5179855035704149e+116

   1. Initial program 19.1

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

   if -1.7987418643598683e-280 < re < 2.4967545228125466e-154

   1. Initial program 29.5

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

   2. Taylor expanded around 0 35.5

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

   if 1.5179855035704149e+116 < re

   1. Initial program 51.1

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

   2. Taylor expanded around inf 9.6

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

4. Final simplification18.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.758999353527392 \cdot 10^{+183}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le -1.7987418643598683 \cdot 10^{-280}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{elif}\;re \le 2.4967545228125466 \cdot 10^{-154}:\\ \;\;\;\;im\\ \mathbf{elif}\;re \le 1.5179855035704149 \cdot 10^{+116}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019002 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 11.6s)Debug log