Details

Time bar (total: 8.9s)

analyze390.0ms (4.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
15.6%31.2%53.2%6
17.2%26.5%56.3%7
18%22.6%59.4%8
18.3%19.9%61.8%9
18.5%17.8%63.7%10
18.6%16.3%65.1%11
18.7%15.2%66.1%12
18.7%14.4%66.9%13
18.7%13.8%67.4%14
Compiler

Compiled 17 to 16 computations (5.9% saved)

sample84.0ms (0.9%)

Algorithm
1×intervals
Results
23.0ms256×body128valid
21.0ms48×body1024nan
13.0ms99×body128overflowed
7.0ms24×body512nan
3.0ms33×body128nan
3.0ms15×body256nan
1.0ms12×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify214.0ms (2.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0490822
1490822

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.3b

Counts
2 → 2
Compiler

Compiled 44 to 41 computations (6.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.2b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b
(*.f64 (*.f64 2 PI.f64) n)

rewrite37.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
48×times-frac_binary64_766
42×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
33×add-cube-cbrt_binary64_795
26×add-exp-log_binary64_798
22×pow-unpow_binary64_837
18×sqrt-prod_binary64_776
14×pow1_binary64_821
10×add-cbrt-cube_binary64_796
9×prod-exp_binary64_809
8×sqr-pow_binary64_732 unpow-prod-down_binary64_839
6×associate-/r*_binary64_704 pow-exp_binary64_828 difference-of-squares_binary64_729 pow-prod-down_binary64_831
5×associate-/l*_binary64_705 div-exp_binary64_811
3×add-log-exp_binary64_799 distribute-lft-out--_binary64_712 associate-*r*_binary64_700 cbrt-unprod_binary64_793 pow-pow_binary64_832
2×div-inv_binary64_757 pow-to-exp_binary64_829 div-sub_binary64_765 pow-sub_binary64_836
1×frac-2neg_binary64_771 cbrt-undiv_binary64_794 associate-/l/_binary64_707 associate-*l*_binary64_701 clear-num_binary64_759 *-commutative_binary64_691
Counts
3 → 115
Calls

3 calls:

11.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)

series494.0ms (5.5%)

Counts
3 → 9
Calls

3 calls:

307.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
147.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
40.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify64.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
054003540

prune194.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New11212124
Fresh011
Picked101
Done000
Total11313126

Merged error: 0.0b

Counts
126 → 13
Compiler

Compiled 3288 to 2255 computations (31.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (*.f64 2 PI.f64) n)

rewrite43.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
127×add-exp-log_binary64_798
67×prod-exp_binary64_809
36×pow-exp_binary64_828
30×div-exp_binary64_811
20×pow1_binary64_821
19×add-cbrt-cube_binary64_796
15×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
14×times-frac_binary64_766
13×pow-unpow_binary64_837
12×pow-to-exp_binary64_829
9×pow-prod-down_binary64_831
7×cbrt-unprod_binary64_793
6×associate-*r*_binary64_700
5×associate-/l*_binary64_705
4×add-log-exp_binary64_799
3×sqr-pow_binary64_732 unpow-prod-down_binary64_839 pow-pow_binary64_832
2×cbrt-undiv_binary64_794 div-inv_binary64_757 associate-*l*_binary64_701 *-commutative_binary64_691
1×frac-2neg_binary64_771 associate-/r*_binary64_704 clear-num_binary64_759
Counts
4 → 118
Calls

4 calls:

11.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
7.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
5.0ms
(*.f64 (*.f64 2 PI.f64) n)

series675.0ms (7.6%)

Counts
4 → 12
Calls

4 calls:

411.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
189.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
39.0ms
(*.f64 (*.f64 2 PI.f64) n)
36.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify68.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
056032652

prune189.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1282130
Fresh21012
Picked101
Done000
Total13112143

Merged error: 0b

Counts
143 → 12
Compiler

Compiled 3437 to 2390 computations (30.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
0.2b
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (*.f64 2 PI.f64) n)

rewrite72.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
284×times-frac_binary64_766
126×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
111×sqrt-prod_binary64_776
33×add-exp-log_binary64_798
28×sqr-pow_binary64_732 unpow-prod-down_binary64_839
24×associate-/l*_binary64_705
20×pow1_binary64_821
19×add-cbrt-cube_binary64_796
11×div-exp_binary64_811
9×prod-exp_binary64_809 pow-prod-down_binary64_831
8×div-inv_binary64_757
6×associate-/r*_binary64_704 associate-*r*_binary64_700 cbrt-unprod_binary64_793
4×add-log-exp_binary64_799
3×cbrt-undiv_binary64_794 sqrt-pow1_binary64_778 pow-exp_binary64_828
2×associate-*l*_binary64_701 *-commutative_binary64_691
1×frac-2neg_binary64_771 associate-/l/_binary64_707 pow-to-exp_binary64_829 pow1/2_binary64_840 clear-num_binary64_759
Counts
4 → 241
Calls

4 calls:

17.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
4.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

series560.0ms (6.3%)

Counts
4 → 12
Calls

4 calls:

444.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
43.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
37.0ms
(*.f64 (*.f64 2 PI.f64) n)
36.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify138.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0509011746

prune552.0ms (6.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2512253
Fresh3811
Picked011
Done000
Total25411265

Merged error: 0b

Counts
265 → 11
Compiler

Compiled 8957 to 5812 computations (35.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 1 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.2b
(*.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (/.f64 1 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (*.f64 2 PI.f64) n)

rewrite69.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
422×add-exp-log_binary64_798
302×prod-exp_binary64_809
111×pow-exp_binary64_828
72×div-exp_binary64_811
37×pow-to-exp_binary64_829
36×rec-exp_binary64_810 1-exp_binary64_804
28×add-cbrt-cube_binary64_796
15×pow1_binary64_821
14×add-sqr-sqrt_binary64_782
13×associate-*r*_binary64_700
11×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 cbrt-unprod_binary64_793
7×associate-*l*_binary64_701
6×pow-prod-down_binary64_831 times-frac_binary64_766
4×cbrt-undiv_binary64_794 add-log-exp_binary64_799
3×associate-/l*_binary64_705 *-commutative_binary64_691
2×unswap-sqr_binary64_728 div-inv_binary64_757 sqr-pow_binary64_732
1×frac-2neg_binary64_771 associate-/r*_binary64_704 inv-pow_binary64_845 associate-*r/_binary64_702 clear-num_binary64_759 un-div-inv_binary64_758 unpow-prod-down_binary64_839 pow-flip_binary64_834
Counts
4 → 197
Calls

4 calls:

16.0ms
(*.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (/.f64 1 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
9.0ms
(/.f64 1 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
6.0ms
(*.f64 (*.f64 2 PI.f64) n)

series753.0ms (8.4%)

Counts
4 → 12
Calls

4 calls:

416.0ms
(*.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (/.f64 1 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
261.0ms
(/.f64 1 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
38.0ms
(*.f64 (*.f64 2 PI.f64) n)
38.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify106.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049665109
149665109

prune282.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2090209
Fresh099
Picked011
Done011
Total20911220

Merged error: 0b

Counts
220 → 11
Compiler

Compiled 4918 to 3376 computations (31.4% saved)

regimes392.0ms (4.4%)

Compiler

Compiled 4734 to 3946 computations (16.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02150
12150

end0.0ms (0%)

sample3.5s (39.1%)

Algorithm
1×intervals
Results
742.0ms8000×body128valid
608.0ms1326×body1024nan
333.0ms2359×body128overflowed
215.0ms692×body512nan
67.0ms1011×body128nan
63.0ms357×body256nan
21.0ms228×body128invalid
Compiler

Compiled 1220 to 1017 computations (16.6% saved)

Profiling

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