THE FORMULA FOR TIME

# The Equation of Time is the difference between our standard clock time and the time that would be based on the exact position of the Sun in the sky, for example, that measured by a sundial.
# The two are different because of two specific reasons:

1. The eccentricity of the Earth's orbit causes us to speed up and slow down in different parts of our annual orbit.
2. The Earth's axis is tilted to our orbit, and so the Sun's apparent motion along the (tilted) Ecliptic has a varying effect when viewed along the Equatorial plane.

After taking care of the conditions of the change in eccentricity of the Earth's orbit and its elliptical nature, the average number of days in a year turn out to be 365.2490448790509.

Using this number, we can calculate as follows:

The program flow was similar to your program with the number of weeks averaged to be = (average number of days in a year)/7. Also the accuracy of pi was taken to 100 digits.

The answer turned out to be equal to 32,758,501.32966996 as against your time_formula answer of 31,545,739.32

MY FORMULA FOR TIME---------
360/7=51.42857143/12.57146=4.0908988864/4=1.022724716*51=52.15896051*7=365.1127236*24=8,762.705366*60*60=31,545,739.32 SECONDS IN A YEAR TAKE AWY FROM THE NUMBER OF SECONDS IN A YEAR WITH ATOMIC SIDEREAL TIME 31,558,515.36 with the right value of Pi.
365.256363051 average days in a sidereal year*86,400 average seconds= 31,558149.76- 31,558,515.36=365.5957 seconds/60=6.093261667
minutes difference in a year..
360/7=51.42857143/12.56637061=4.092555681/4=1.02313892*51=52.18008493*7=365.2605945*24=8766.254269*60*60=31,558,515.37.
31,558.149.76=365.61/60=6.0935..

31,558149.76-31,558,515.37= 365.91/60=6.0985