Acc based on Statistical Accuracy

[tr3sleches]

I'm going to be off/away for a while, so I wanted to get this out there.
So I wrote up a statistically accurate accuracy pp type thing.
Mad props to Full Tablet for the inspiration.
I discussed this a long time ago (before I knew this discord even existed), but never got around to doing anything about it:
https://osu.ppy.sh/community/forums/topics/727540?start=6741333
(Ignore my ignorance in this post)

precision = 0.01;
p = 1.645; //based on z-score values
double sGuess(acc,OD)
{
     //approximate mean and standard deviation for OD slope
     u1 = -6.635;
     o1 = 1/0.518926;
     // approximate mean and standard deviation OD intercept
     u2 = 88.485;
     o2 = 1/0.0386966;
     return (u1 + erfinv(2*acc – 1)*o1*Math.sqrt(2))*OD +  (u2 - erfinv(2*acc – 1)*o2*Math.sqrt(2));
}
double E(s,MS)
{
     return erf(MS/(Math.sqrt(2)*s));
}
double E300 = E(s,79.5-6*OD); 
double E100 = E(s,139.5-8*OD); 
double E50 = E(s,199.5-10*OD);
double mean(s,OD)
{
     return (2/3)*E300(s,OD) + (1/6)*E100(s,OD) +(1/6)*E50(s,OD);
}
double Ex2(s,OD)
{
     return (8/9)*E300(s,OD) + (1/12)*E100(s,OD) +(1/36)*E50(s,OD);
}
double sd(s,OD)
{
     return Math.sqrt(Ex2(s,OD) – Math.pow(mean(s,OD),2));
}
double f(acc,num_circles,s,OD)
{
     return acc - mean(s,OD) – Math.sqrt(2/num_circles) * p * sd(s,OD);
}

double bijectionS(acc,num_circles,OD)
{
//initial guesses
double s0;
double s1;
s0 = sGuess(acc,OD);
s1 = sGuess(acc – Math.sqrt(2/(num_circles-1))*p,OD);
//approximation

while(abs(s1-s0) > precision)
{
     if(f(acc,num_circles,(s0+s1)/2,OD)* f(acc,num_circles,s0,OD) > 0)
     {
          s0 = (s0+s1)/2;
     }
     else if(f(acc,num_circles,(s0+s1)/2,OD)* f(acc,num_circles,s1,OD) > 0)
     {
          s1 = (s0+s1)/2;
     }
}
return 0.5 * (s0 + s1);
}

The hard part is finding the function for the acc pp in terms of s.
Ideally we could just directly convert the OD part and be done with it.
2.83*1.52163^OD => a*1.52163^(13.25-s/6) for some constant a.
Although warranted, this could lead to some big changes for decent accuracies.
I don't know how the error function and error inverse function are established in osu, so I just labeled them as erf and erfinv respectively.
I shorthanded some stuff here for clarity, but for actual coding some stuff will have to change, e.g. E300, E100, & E50 might have to be defined like E is instead of shorthanded like it is. I have to fix the inputs of the functions (putting their data type before and such, but that can easily be done later).