\[\left(\left((e^{d} - 1)^* \cdot c\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
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: 25.6 s
Input Error: 35.6
Output Error: 35.7
Log: ⚲
Profile: 🕒
\(\left(\left((e^{(e^{\log_* (1 + \log_* (1 + (e^{d} - 1)^* \cdot c))} - 1)^*} - 1)^*\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\)
  1. Started with
    \[\left(\left((e^{d} - 1)^* \cdot c\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    35.6
  2. Using strategy rm
    35.6
  3. Applied expm1-log1p-u to get
    \[\left(\color{red}{\left((e^{d} - 1)^* \cdot c\right)} \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\color{blue}{\left((e^{\log_* (1 + (e^{d} - 1)^* \cdot c)} - 1)^*\right)} \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    35.7
  4. Using strategy rm
    35.7
  5. Applied expm1-log1p-u to get
    \[\left(\left((e^{\color{red}{\log_* (1 + (e^{d} - 1)^* \cdot c)}} - 1)^*\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\left((e^{\color{blue}{(e^{\log_* (1 + \log_* (1 + (e^{d} - 1)^* \cdot c))} - 1)^*}} - 1)^*\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    35.7

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)))