\[\left(\left((e^{d} - 1)^* \cdot c\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
Test:
(fmod (* (expm1 d) c) (atan2 8.61318337292339e-131 d))
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 2.7 m
Input Error: 17.8
Output Error: 18.3
Log: ⚲
Profile: 🕒
\(\left(\left({\left({\left(\sqrt{\sqrt{(e^{d} - 1)^* \cdot c}}\right)}^2\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\)
  1. Started with
    \[\left(\left((e^{d} - 1)^* \cdot c\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    17.8
  2. Using strategy rm
    17.8
  3. Applied add-sqr-sqrt to get
    \[\left(\color{red}{\left((e^{d} - 1)^* \cdot c\right)} \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\color{blue}{\left({\left(\sqrt{(e^{d} - 1)^* \cdot c}\right)}^2\right)} \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    18.0
  4. Using strategy rm
    18.0
  5. Applied add-sqr-sqrt to get
    \[\left(\left({\color{red}{\left(\sqrt{(e^{d} - 1)^* \cdot c}\right)}}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\left({\color{blue}{\left({\left(\sqrt{\sqrt{(e^{d} - 1)^* \cdot c}}\right)}^2\right)}}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    18.3
  6. Removed slow pow expressions

Original test:


(lambda ((a default) (b default) (c default) (d default))
  #:name "(fmod (* (expm1 d) c) (atan2 8.61318337292339e-131 d))"
  (fmod (* (expm1 d) c) (atan2 8.61318337292339e-131 d)))