\[\tan^{-1}_* \frac{b + \left(-b\right)}{\left(b - 7.078918604288237 \cdot 10^{+238}\right) + 1.3789227555638566 \cdot 10^{+245}}\]
Test:
(atan2 (+ b (- b)) (+ (- b 7.078918604288237e+238) 1.3789227555638566e+245))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 1.6 s
Input Error: 31.0
Output Error: 0
Log: ⚲
Profile: 🕒
\(\tan^{-1}_* \frac{b + \left(-b\right)}{b + 1.3789220476719961 \cdot 10^{+245}}\)
  1. Started with
    \[\tan^{-1}_* \frac{b + \left(-b\right)}{\left(b - 7.078918604288237 \cdot 10^{+238}\right) + 1.3789227555638566 \cdot 10^{+245}}\]
    31.0
  2. Applied taylor to get
    \[\tan^{-1}_* \frac{b + \left(-b\right)}{\left(b - 7.078918604288237 \cdot 10^{+238}\right) + 1.3789227555638566 \cdot 10^{+245}} \leadsto \tan^{-1}_* \frac{b + \left(-b\right)}{b + 1.3789220476719961 \cdot 10^{+245}}\]
    0
  3. Taylor expanded around 0 to get
    \[\tan^{-1}_* \frac{b + \left(-b\right)}{\color{red}{b + 1.3789220476719961 \cdot 10^{+245}}} \leadsto \tan^{-1}_* \frac{b + \left(-b\right)}{\color{blue}{b + 1.3789220476719961 \cdot 10^{+245}}}\]
    0

Original test:


(lambda ((a default) (b default))
  #:name "(atan2 (+ b (- b)) (+ (- b 7.078918604288237e+238) 1.3789227555638566e+245))"
  (atan2 (+ b (- b)) (+ (- b 7.078918604288237e+238) 1.3789227555638566e+245)))