MathBot functions

!math1
==
RealDistance(bx,bz) = if(bz==0, bx-0.6, sqrt((bx-0.6)^2 + (bz-0.6)^2)),
RealMomentum(bx,bz) = if(bz==0, bx+0.6, sqrt((bx+0.6)^2 + (bz+0.6)^2)),
Tier(t) = 12 - t,

Sprint(v) = 0.91 * 0.6 * v + 0.1274,
Sprint_land(v) = 0.91 * v + 0.1274,
Sprint_air(v) = 0.91 * v + 0.02548,
Sprint45(v) = 0.91 * 0.6 * v + 0.13,
Sprint45_land(v) = 0.91 * v + 0.13,
Sprint45_air(v) = 0.91 * v + 0.026,
Walk(v) = 0.91 * 0.6 * v + 0.098,
Walk_land(v) = 0.91 * v + 0.098,
Walk_air(v) = 0.91 * v + 0.0196,
Walk45(v) = 0.91 * 0.6 * v + 0.1,
Walk45_land(v) = 0.91 * v + 0.1,
Walk45_air(v) = 0.91 * v + 0.02,
Sneak(v) = 0.91 * 0.6 * v + 0.0294,
Sneak_land(v) = 0.91 * v + 0.0294,
Sneak_air(v) = 0.91 * v + 0.00588,
Sneak45(v) = 0.91 * 0.6 * v + 0.0294 * sqrt(2),
Sneak45_land(v) = 0.91 * v + 0.0294 * sqrt(2),
Sneak45_air(v) = 0.91 * v + 0.00588 * sqrt(2),
Stop(v) = 0.6 * 0.91 * v,
Stop_land(v) = 0.91 * v,
Stop_air(v) = 0.91 * v,

MAX_SPRINT = 0.1274/0.454,
MAX_SPRINT_AIR = 0.02548/0.09,
MAX_SPRINT45 = 0.13/0.454,
MAX_SPRINT45_AIR = 0.026/0.09,
MAX_WALK = 0.098/0.454,
MAX_WALK_AIR = 0.0196/0.09,
MAX_WALK45 = 0.1/0.454,
MAX_WALK45_AIR = 0.02/0.09,
MAX_SNEAK = 0.0294/0.454,
MAX_SNEAK_AIR = 0.00588/0.09,
MAX_SNEAK45 = sqrt(2) * 0.0294/0.454,
MAX_SNEAK45_AIR = sqrt(2) * 0.00588/0.09,

Vy_new(t) = 0.42 * 0.98^(t-1) + 4 * 0.98^t - 3.92,
Height_new(t) = 217 * (1-0.98^t) - 3.92 * t,
Vy(t) = if(t<6, Vy_new(t), 4 * 0.98^(t-5) - 3.92),
Height(t) = if(t<6, Height_new(t), Height_new(5) + 200 * (0.98 - 0.98^(t-4)) - 3.92 * (t-5)),
DurationRec(h,y,t,vy) = if(y>h, DurationRec(h,y+vy,t+1,vy * 0.98 - 0.0784), t),
Duration(h) = if(h>Height(6), -1, DurationRec(h,Height(6),5,0)),
Duration_new(h) = if(h>Height(6), -1, DurationRec(h,Height(6),5,Vy_new(6)))

!math2
==
Vh(v,t,J,M) = ifelse(t==0,v,t==1,0.91 * v,2 * M/9 + (0.6 * 0.91^t) * (v+J/0.91-0.02 * M/0.04914)),
Vh_del(v,t,J,M) = ifelse(t==0,v,t==1,0.546 * v,2 * M/9 + (0.6 * 0.91^t) * (0.6 * v +J/0.91-0.02 * M/0.04914)),
Sprintjump(v,t) = Vh(v,t,0.3274,1.274),
Sprintjump_del(v,t) = Vh_del(v,t,0.3274,1.274),
Sprintjump45(v,t) = Vh(v,t,0.3274,1.3),
Sprintjump45_del(v,t) = Vh_del(v,t,0.3274,1.3),
Walkjump(v,t) = Vh(v,t,0.098,0.98),
Walkjump_del(v,t) = Vh_del(v,t,0.098,0.98),
Walkjump45(v,t) = Vh(v,t,0.1,1.0),
Walkjump45_del(v,t) = Vh_del(v,t,0.1,1.0),
Strafejump(v,t) = Vh(v,t,0.2+0.13/sqrt(2),1.274),
Strafejump_del(v,t) = Vh_del(v,t,0.2+0.13/sqrt(2),1.274),
Strafejump45(v,t) = Vh(v,t,0.2+0.13/sqrt(2),1.3),
Strafejump45_del(v,t) = Vh_del(v,t,0.2+0.13/sqrt(2),1.3),

Chain(v,t,J,M,n) = v * (0.6 * 0.91^t)^n + (J * 0.6 * 0.91^(t-1)+2 * M * (1-0.91^(t-1))/9) * (1-(0.6 * 0.91^t)^n)/(1-0.6 * 0.91^t),
Chain_del(v,t,J,M,n) = 0.6 * v * (0.6 * 0.91^t)^n + (J * 0.6 * 0.91^(t-1)+2 * M * (1-0.91^(t-1))/9) * (1-(0.6 * 0.91^t)^n)/(1-0.6 * 0.91^t),
Chain_Sprintjump(v,t,n) = Chain(v,t,0.3274,1.274,n),
Chain_Sprintjump_del(v,t,n) = Chain_del(v,t,0.3274,1.274,n),
Chain_Sprintjump45(v,t,n) = Chain(v,t,0.3274,1.3,n),
Chain_Sprintjump45_del(v,t,n) = Chain_del(v,t,0.3274,1.3,n),
Chain_Walkjump(v,t,n) = Chain(v,t,0.098,0.98,n),
Chain_Walkjump_del(v,t,n) = Chain_del(v,t,0.098,0.98,n),
Chain_Walkjump45(v,t,n) = Chain(v,t,0.1,1.0,n),
Chain_Walkjump45_del(v,t,n) = Chain_del(v,t,0.1,1.0,n),

Max_Chain(t,J,M) = (J * 0.6 * 0.91^(t-1)+2 * M * (1-0.91^(t-1))/9) / (1-0.6 * 0.91^t),
Max_Sprintjump(t) = Max_Chain(t,0.3274,1.274),
Max_Sprintjump45(t) = Max_Chain(t,0.3274,1.3),
Max_Walkjump(t) = Max_Chain(t,0.098,0.98),
Max_Walkjump45(t) = Max_Chain(t,0.1,1.0)


!math3
==
Dist(v,t,J,M) = ifelse(t<1,0,t==1, v, 1.91 * v + J + 2 * M * (t-2)/9 + (0.49686/0.09) * (1-0.91^(t-2)) * (v + J/0.91 - 0.02 * M/0.04914)),
Dist_del(v,t,J,M) = ifelse(t<1,0,t==1, v, 1.546 * v + J + 2 * M * (t-2)/9 + (0.49686/0.09) * (1-0.91^(t-2)) * (0.6 * v + J/0.91 - 0.02 * M/0.04914)),
Dist_Sprintjump(v,t) = Dist(v,t,0.3274,1.274),
Dist_Sprintjump_del(v,t) = Dist_del(v,t,0.3274,1.274),
Dist_Sprintjump45(v,t) = Dist(v,t,0.3274,1.3),
Dist_Sprintjump45_del(v,t) = Dist_del(v,t,0.3274,1.3),
Dist_Walkjump(v,t) = Dist(v,t,0.098,0.98),
Dist_Walkjump_del(v,t) = Dist_del(v,t,0.098,0.98),
Dist_Walkjump45(v,t) = Dist(v,t,0.1,1.0),
Dist_Walkjump45_del(v,t) = Dist_del(v,t,0.1,1.0),
Dist_Strafejump(v,t) = Dist(v,t,0.2+0.13/sqrt(2),1.274),
Dist_Strafejump_del(v,t) = Dist_del(v,t,0.2+0.13/sqrt(2),1.274),
Dist_Strafejump45(v,t) = Dist(v,t,0.2+0.13/sqrt(2),1.3),
Dist_Strafejump45_del(v,t) = Dist_del(v,t,0.2+0.13/sqrt(2),1.3),

SpeedReq(d,t,J,M) = ifelse(t<1,0,t==1, d, (d-(J+ 2 * M * (t-2)/9 + (0.91 - 0.91^(t-1)) * (J * 0.6 - 2 * M/9)/0.09)) / (1.91 + 0.6 * (0.8281-0.91^t)/0.09)),
SpeedReq_del(d,t,J,M) = ifelse(t<1,0,t==1, d, (d-(J+ 2 * M * (t-2)/9 + (0.91 - 0.91^(t-1)) * (J * 0.6 - 2 * M/9)/0.09)) / (1.546 + 0.36 * (0.8281-0.91^t)/0.09)),
SpeedReq_Sprintjump(d,t) = SpeedReq(d,t,0.3274,1.274),
SpeedReq_Sprintjump_del(d,t) = SpeedReq_del(d,t,0.3274,1.274),
SpeedReq_Sprintjump45(d,t) = SpeedReq(d,t,0.3274,1.3),
SpeedReq_Sprintjump45_del(d,t) = SpeedReq_del(d,t,0.3274,1.3),
SpeedReq_Walkjump(d,t) = SpeedReq(d,t,0.098,0.98),
SpeedReq_Walkjump_del(d,t) = SpeedReq_del(d,t,0.098,0.98),
SpeedReq_Walkjump45(d,t) = SpeedReq(d,t,0.1,1.0),
SpeedReq_Walkjump45_del(d,t) = SpeedReq_del(d,t,0.1,1.0),
SpeedReq_Strafejump(d,t) = SpeedReq(d,t,0.2+0.13/sqrt(2),1.274),
SpeedReq_Strafejump_del(d,t) = SpeedReq_del(d,t,0.2+0.13/sqrt(2),1.274),
SpeedReq_Strafejump45(d,t) = SpeedReq(d,t,0.2+0.13/sqrt(2),1.3),
SpeedReq_Strafejump45_del(d,t) = SpeedReq_del(d,t,0.2+0.13/sqrt(2),1.3)