\[\left(\left((e^{d} - 1)^* \cdot c\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
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: 4.0 s
Input Error: 28.4
Output Error: 15.7
Log: ⚲
Profile: 🕒
\(\left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{\frac{-1}{d}}\right)\right)\)
  1. Started with
    \[\left(\left((e^{d} - 1)^* \cdot c\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    28.4
  2. Using strategy rm
    28.4
  3. Applied add-sqr-sqrt to get
    \[\left(\color{red}{\left((e^{d} - 1)^* \cdot c\right)} \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\color{blue}{\left({\left(\sqrt{(e^{d} - 1)^* \cdot c}\right)}^2\right)} \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    29.0
  4. Using strategy rm
    29.0
  5. Applied add-cube-cbrt to get
    \[\left(\left({\left(\sqrt{\color{red}{(e^{d} - 1)^* \cdot c}}\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\left({\left(\sqrt{\color{blue}{{\left(\sqrt[3]{(e^{d} - 1)^* \cdot c}\right)}^3}}\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    29.0
  6. Applied taylor to get
    \[\left(\left({\left(\sqrt{{\left(\sqrt[3]{(e^{d} - 1)^* \cdot c}\right)}^3}\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\left({\left(\sqrt{0}\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    15.3
  7. Taylor expanded around inf to get
    \[\left(\left({\left(\sqrt{\color{red}{0}}\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(\left({\left(\sqrt{\color{blue}{0}}\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)\]
    15.3
  8. Applied simplify to get
    \[\color{red}{\left(\left({\left(\sqrt{0}\right)}^2\right) \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)} \leadsto \color{blue}{\left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right)}\]
    15.3
  9. Applied taylor to get
    \[\left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{d}\right)\right) \leadsto \left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{\frac{-1}{d}}\right)\right)\]
    15.7
  10. Taylor expanded around -inf to get
    \[\color{red}{\left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{\frac{-1}{d}}\right)\right)} \leadsto \color{blue}{\left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{\frac{-1}{d}}\right)\right)}\]
    15.7
  11. Applied simplify to get
    \[\left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{\frac{-1}{d}}\right)\right) \leadsto \left(0 \bmod \left(\tan^{-1}_* \frac{8.61318337292339 \cdot 10^{-131}}{\frac{-1}{d}}\right)\right)\]
    15.7
  12. Applied final simplification

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)))