No reevaluation of evaluated values

[poke1024]

Mathics currently reevaluates variable values (i.e. values of symbols set via Set[]) every time they're accessed.

This can lead to some worrisome performance (and it gets worse for even longer lists):

x=Range[10000]; Timing[First[x]]
{0.2507470000000005,1}

This PR fixes this by not rebuilding expressions if no var is replaced. That way, the original expression's is_evaluated attribute does not get reset, and the expression is thus not reevaluated when Expression.evaluate() gets called for it later on. With change in PR:

x=Range[10000]; Timing[First[x]]
{0.08288399999999996,1}

[bnjones]

Can you run benchmark.py before/after to see if this improves performance across the board?

[bnjones]

Why len(vars) == 0 instead of not vars?

[poke1024]

Good point, I wasn't even aware that not could be used in this way on a dict here. Changed that.

[poke1024]

benchmark.py seems to give a very slight across the board improvement of 2-4%, but it could be as well random noise. I think it really only affects the special case of looking up a symbol that's expensive to compute.

EDIT I looked at best, when I should have looked at avg. Now it seems more like 10% to 15% improvement. Here are the values:

EVALUATION BENCHMARKS (WITH PR CHANGE):
Arithmetic
  '1 + 2'
     5000 loops, avg:  227 us per loop, best:  209 us per loop
  '5 * 3'
     5000 loops, avg:  246 us per loop, best:  223 us per loop

DensityPlot
  'DensityPlot[x + y^2, {x, -3, 3}, {y, -2, 2}]'
        5 loops, avg:  489 ms per loop, best:  378 ms per loop

Expand
  'Expand[(a1+a2)^200]'
        5 loops, avg:  424 ms per loop, best:  328 ms per loop
  'Expand[(a1+a2+a3)^25]'
        5 loops, avg:  883 ms per loop, best:  695 ms per loop
  'Expand[(a1+a2+a3+a4+a5+a6+a7)^3]'
       10 loops, avg:  152 ms per loop, best:  125 ms per loop

Matrix
  'RandomInteger[{0,1}, {10,10}] . RandomInteger[{0,1}, {10,10}]'
        5 loops, avg:  403 ms per loop, best:  315 ms per loop
  'RandomInteger[{0,10}, {10,10}] + RandomInteger[{0,10}, {10,10}]'
      100 loops, avg: 38.4 ms per loop, best: 35.8 ms per loop

Plot
  'Plot[0, {x, -3, 3}]'
      100 loops, avg: 92.4 ms per loop, best: 87.7 ms per loop
  'Plot[x^2 + x + 1, {x, -3, 3}]'
        5 loops, avg:  820 ms per loop, best:  664 ms per loop
  'Plot[Sin[Cos[x^2]], {x, -3, 3}]'
        5 loops, avg: 2.46 s  per loop, best: 2.03 s  per loop
  'Plot[Sin[100 x], {x, -3, 3}]'
        5 loops, avg: 1.75 s  per loop, best: 1.43 s  per loop

Plot3D
  'Plot3D[0, {x, -1, 1}, {y, -1, 1}]'
        5 loops, avg:  264 ms per loop, best:  205 ms per loop
  'Plot3D[x + y^2, {x, -3, 3}, {y, -2, 2}]'
        5 loops, avg:  822 ms per loop, best:  639 ms per loop
  'Plot3D[Sin[x + y^2], {x, -3, 3}, {y, -3, 3}]'
        5 loops, avg: 2.55 s  per loop, best: 2.08 s  per loop
  'Plot3D[Sin[100 x + 100 y ^ 2], {x, 0, 1}, {y, 0, 1}]'
        5 loops, avg: 2.83 s  per loop, best: 2.14 s  per loop

Random
  'RandomInteger[{-100, 100}, 100]'
     1000 loops, avg: 5.82 ms per loop, best: 3.94 ms per loop
  'RandomInteger[10, {10, 10}]'
     1000 loops, avg: 5.83 ms per loop, best: 4.59 ms per loop
  'RandomInteger[{0,1}, {5, 5, 5}]'
     1000 loops, avg: 7.77 ms per loop, best: 6.22 ms per loop
  'RandomReal[1, 100]'
     1000 loops, avg: 7.88 ms per loop, best: 6.37 ms per loop
  'RandomReal[{-1, 1}, 100]'
     1000 loops, avg: 7.57 ms per loop, best: 6.21 ms per loop
  'RandomComplex[2 + I, 50]'
      100 loops, avg: 37.1 ms per loop, best: 29.5 ms per loop
  'RandomComplex[{-1 - I, 1 + I}, {10, 10}]'
      100 loops, avg: 65.9 ms per loop, best: 58.6 ms per loop

Trig
  'Sin[RandomReal[]]'
     1000 loops, avg: 1.97 ms per loop, best: 1.67 ms per loop
  'ArcTan[RandomReal[]]'
     1000 loops, avg: 1.79 ms per loop, best: 1.55 ms per loop

    EVALUATION BENCHMARKS (WITHOUT PR CHANGE):
Arithmetic
  '1 + 2'
     5000 loops, avg:  236 us per loop, best:  210 us per loop
  '5 * 3'
     5000 loops, avg:  289 us per loop, best:  226 us per loop

DensityPlot
  'DensityPlot[x + y^2, {x, -3, 3}, {y, -2, 2}]'
        5 loops, avg:  492 ms per loop, best:  370 ms per loop

Expand
  'Expand[(a1+a2)^200]'
        5 loops, avg:  471 ms per loop, best:  373 ms per loop
  'Expand[(a1+a2+a3)^25]'
        5 loops, avg: 1.02 s  per loop, best:  765 ms per loop
  'Expand[(a1+a2+a3+a4+a5+a6+a7)^3]'
       10 loops, avg:  173 ms per loop, best:  132 ms per loop

Matrix
  'RandomInteger[{0,1}, {10,10}] . RandomInteger[{0,1}, {10,10}]'
        5 loops, avg:  447 ms per loop, best:  353 ms per loop
  'RandomInteger[{0,10}, {10,10}] + RandomInteger[{0,10}, {10,10}]'
      100 loops, avg: 42.3 ms per loop, best: 36.1 ms per loop

Plot
  'Plot[0, {x, -3, 3}]'
       10 loops, avg:  118 ms per loop, best: 89.5 ms per loop
  'Plot[x^2 + x + 1, {x, -3, 3}]'
        5 loops, avg:  833 ms per loop, best:  663 ms per loop
  'Plot[Sin[Cos[x^2]], {x, -3, 3}]'
        5 loops, avg: 2.76 s  per loop, best: 2.26 s  per loop
  'Plot[Sin[100 x], {x, -3, 3}]'
        5 loops, avg: 1.86 s  per loop, best: 1.49 s  per loop

Plot3D
  'Plot3D[0, {x, -1, 1}, {y, -1, 1}]'
        5 loops, avg:  287 ms per loop, best:  216 ms per loop
  'Plot3D[x + y^2, {x, -3, 3}, {y, -2, 2}]'
        5 loops, avg:  859 ms per loop, best:  641 ms per loop
  'Plot3D[Sin[x + y^2], {x, -3, 3}, {y, -3, 3}]'
        5 loops, avg: 2.74 s  per loop, best: 2.16 s  per loop
  'Plot3D[Sin[100 x + 100 y ^ 2], {x, 0, 1}, {y, 0, 1}]'
        5 loops, avg: 2.85 s  per loop, best: 2.19 s  per loop

Random
  'RandomInteger[{-100, 100}, 100]'
     1000 loops, avg: 4.73 ms per loop, best: 3.99 ms per loop
  'RandomInteger[10, {10, 10}]'
     1000 loops, avg: 6.18 ms per loop, best: 4.64 ms per loop
  'RandomInteger[{0,1}, {5, 5, 5}]'
     1000 loops, avg: 7.21 ms per loop, best: 6.28 ms per loop
  'RandomReal[1, 100]'
     1000 loops, avg: 7.26 ms per loop, best: 6.39 ms per loop
  'RandomReal[{-1, 1}, 100]'
     1000 loops, avg: 6.87 ms per loop, best: 6.23 ms per loop
  'RandomComplex[2 + I, 50]'
      100 loops, avg: 32.6 ms per loop, best: 29.6 ms per loop
  'RandomComplex[{-1 - I, 1 + I}, {10, 10}]'
      100 loops, avg: 63.6 ms per loop, best: 59.5 ms per loop

Trig
  'Sin[RandomReal[]]'
     1000 loops, avg: 1.78 ms per loop, best:  1.7 ms per loop
  'ArcTan[RandomReal[]]'
     1000 loops, avg: 1.65 ms per loop, best: 1.57 ms per loop