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How to make NSolve faster?

Can somebody help me, to make these program faster? u and r are parameters, a,b,c,d,q,w,Ca are variables. I need to numerical solve these system for many values of u and r. And it take 10 seconds for every values of r and u. Can I make it faster?

u = 1.9; j = 1; While[u <= 4, u = u + 0.1; r = 0;  While [r <= 0.1, r = r + 0.001;   s1[[j++]] =     NSolve[{Ca/u^2 +         r (6 a (c^2 - d^2) + 12 b c d +            6 (q^2 + w^2 + a^2 + b^2 + c^2 + d^2) Ca + Ca^3) == 0,      a (1/u^2 - 1) + r (3 a (a^2 + b^2) + 6 a (c^2 + d^2) -            3 w^2 q + q^3 + 6 a (q^2 + w^2) + 3 c^2 Ca - 3 d^2 Ca +            3 a Ca^2) == 0.5,      b (1/u^2 - 1) +         r (3 b (a^2 + b^2) + 6 b (c^2 + d^2) - w^3 + 3 w q^2 +            6 b (q^2 + w^2) + 6 c d Ca + 3 b Ca^2) == 0,      c (1/u^2 - 0.25) +         r (6 (a^2 + b^2) c + 3 c (c^2 + d^2) + 6 c (q^2 + w^2) +            6 (a c + b d) Ca + 3 c Ca^2) == 0,      d (1/u^2 - 0.25) +         r (6 (a^2 + b^2) d + 3 d (c^2 + d^2) + 6 d (q^2 + w^2) +            6 (-a d + b c) Ca + 3 d Ca^2) == 0,      q (1/u^2 - 0.25) +         r (6 (a^2 + b^2) q + 6 (c^2 + d^2) q + 3 q (q^2 + w^2) +            3 (a q^2 - a w^2 + 2 b q w) + 3 q Ca^2) == 0,      w (1/u^2 - 0.25) +         r (6 (a^2 + b^2) w + 6 (c^2 + d^2) w + 3 w (q^2 + w^2) +            3 (-2 a q w + b q^2 - b w^2) + 3 w Ca^2) == 0      }, {a, b, c, d, q, w, Ca}, Reals, VerifySolutions -> False]];] 

When you get extra turns or dash actions, can you go faster?

The answer to the Amazing Lightspeed Horse exploit seems to indicate that no matter how many turns you get in a round (and thus no matter how many actions you get), you should only be allowed to move twice your speed after using at least one dash action, other dash actions being wasted.

Rogues get dash actions as bonus actions via ‘cunning action’, allowing them to potentially use two dash actions in a single round starting at level two. When I’ve played and GMed I’ve certainly allowed that to let people go thrice speed rather than double, for the same reasons explained in our question on that topic. Thieves also get an extra turn each first-round-of-combat at level 17, from Thief’s Reflexes, whose dashes I would also allow to move them up to their speed each, and who I would probably also have let move an extra set of movement for free.

This seems to contradict the highly upvoted and accepted answer claiming that no creature can ever for any reason use more than its speed in movement in a single round, though (except for a single dash action because ???).

Which interpretation is correct?

Can a creature with wings choose to fall to get down faster?

A dragon flies at 4000 feet of altitude and needs to get to ground level as fast as possible.

With a double-move and a fly speed of 200, it can only move 400 feet per round.

But, can it choose to stop flapping its wings and fall (I would assume maybe 500 or 1000 feet per round), and then use the Fly skill to negate the 20d6 of falling damage when it hits the ground?

Why is ALTER faster than UPDATE?

Let’s create a garbage table..

CREATE TABLE foo   AS SELECT x::text FROM generate_series(1,20e6) AS t(x);  Time: 14077.654 ms (00:14.078) 

Now, let’s look at boring UPDATE,

UPDATE foo SET x = 'foo'; Time: 22239.050 ms (00:22.239) 

Compared with ALTER,

ALTER TABLE foo   ALTER COLUMN x   SET DATA TYPE text   USING 'foo'; Time: 9480.027 ms (00:09.480) 

It’s approximately twice as fast.

Faster computation of $ke^{-(x – h)^2}$

The question is quite simple; almost every computer language today provides the $ \exp(x)$ function in their standard library to compute expressions like $ ke^{-(x – h)^2}.$ However, I would like to know whether this function is the fastest way to compute the above expression. In other words, is there some way to compute $ ke^{-(x – h)^2}$ faster than $ \exp(x)$ in standard libraries while keeping the result very accurate?

I would like to specify that Taylor series will not work for my application, nor will any other polynomial approximations.

Can multiple casters combine Flesh to Stone to petrify a target faster?

The flesh to stone spell states:

A creature restrained by this spell must make another Constitution saving throw at the end of each of its turns. If it successfully saves against this spell three times, the spell ends. If it fails its saves three times, it is turned to stone and subjected to the petrified condition for the duration. The successes and failures don’t need to be consecutive; keep track of both until the target collects three of a kind.

Say a wizard casts flesh to stone on an enemy, an orc to make it simple, and the orc fails the first saving throw.

Then the wizards friend, in the same round, casts a second flesh to stone spell on the poor orc, to which he also fails his saving throw. Then the wizards other friend casts a third flesh to stone in that same round on the poor orc and he fails that saving throw as well.

Does the orc fully petrify in that round? In other words, do the effects of the spells starting to petrify the orc stack with each other? He did fail 3 saving throws but it was against 3 separate spells instead of one spell.

Is it a useful strategy for Mobile VR titles to render faster than their simulation loop?

For example – If a title had a very heavy simulation loop (say 20ms), is it desirable to render at a greater rate, say 90hz?

This would always a present head pose correct to the view, without being stalled on simulation.

Or does this result in discomfort for the player, and instead render and sim should stay in lockstep?

Batching multiple nearest surface queries: Is it faster? Are there better algorithms?

I’m working on an algorithm that computes lots of "nearest point on a triangulated surface" queries in 3d as a way to resample data sets, and I’m wondering if there is any information out there on speeding up these queries. My gut tells me that partitioning the set of query points in a voxel grid or something, and doing them in batches could be a speedup, but I can’t quite see how I could efficiently use that. Also I’m not sure if the time cost of partitioning would balance the search speedup. Is running N independent queries really the best way?

I found that there are papers and research for the all-knn algorithm, but that’s for searching within a single set. And then, those speedups take advantage of the previously computed neighbors or structure within the single set, so I can’t use them. It feels close though.

Any help is appreciated.