Details

Time bar (total: 11.7s)

analyze382.0ms (3.3%)

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)

sample68.0ms (0.6%)

Algorithm
1×intervals
Results
22.0ms256×body128valid
16.0ms36×body1024nan
9.0ms67×body128overflowed
3.0ms11×body512nan
2.0ms10×body256nan
2.0ms32×body128nan
1.0ms13×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify215.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0490822
1490822

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

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

rewrite40.0ms (0.3%)

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))
8.0ms
(/.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)

series498.0ms (4.3%)

Counts
3 → 9
Calls

3 calls:

305.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
156.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
36.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify60.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
054003540

prune198.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11311124
Fresh101
Picked101
Done000
Total11511126

Merged error: 0.0b

Counts
126 → 11
Compiler

Compiled 3212 to 2197 computations (31.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite71.0ms (0.6%)

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:

18.0ms
(/.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))

series573.0ms (4.9%)

Counts
4 → 12
Calls

4 calls:

453.0ms
(/.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))
40.0ms
(*.f64 (*.f64 2 PI.f64) n)
37.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify128.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
0509011746

prune538.0ms (4.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2494253
Fresh4610
Picked011
Done000
Total25311264

Merged error: 0.0b

Counts
264 → 11
Compiler

Compiled 8949 to 5803 computations (35.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
1.0b
(sqrt.f64 (*.f64 2 PI.f64))

rewrite225.0ms (1.9%)

Algorithm
1×rewrite-expression-head
Rules
480×times-frac_binary64_766
306×add-sqr-sqrt_binary64_782
225×sqrt-prod_binary64_776 add-exp-log_binary64_798
214×associate-*r*_binary64_700
187×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795
101×div-exp_binary64_811
87×prod-exp_binary64_809
63×sqr-pow_binary64_732
40×unpow-prod-down_binary64_839
39×pow-exp_binary64_828
35×add-cbrt-cube_binary64_796
33×unswap-sqr_binary64_728
26×associate-*l*_binary64_701
19×pow1_binary64_821
13×pow-to-exp_binary64_829
12×cbrt-unprod_binary64_793
9×cbrt-undiv_binary64_794
8×div-inv_binary64_757 pow-prod-down_binary64_831
4×add-log-exp_binary64_799
3×*-commutative_binary64_691
2×sqrt-pow1_binary64_778
1×associate-*l/_binary64_703 frac-times_binary64_770 associate-*r/_binary64_702 pow1/2_binary64_840
Counts
4 → 372
Calls

4 calls:

130.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
2.0ms
(sqrt.f64 (*.f64 2 PI.f64))

series807.0ms (6.9%)

Counts
4 → 10
Calls

4 calls:

725.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
42.0ms
(*.f64 (*.f64 2 PI.f64) n)
39.0ms
(*.f64 (*.f64 2 PI.f64) n)
0.0ms
(sqrt.f64 (*.f64 2 PI.f64))

simplify163.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
382 → 382
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0501018694

prune1.3s (11.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3811382
Fresh369
Picked011
Done011
Total3849393

Merged error: 0b

Counts
393 → 9
Compiler

Compiled 17071 to 10489 computations (38.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
1.0b
(sqrt.f64 PI.f64)

rewrite184.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
444×add-exp-log_binary64_798
407×times-frac_binary64_766
217×add-sqr-sqrt_binary64_782
214×associate-*r*_binary64_700
204×sqrt-prod_binary64_776
193×prod-exp_binary64_809
191×div-exp_binary64_811
180×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795
75×pow-exp_binary64_828
50×add-cbrt-cube_binary64_796
41×sqr-pow_binary64_732
37×unpow-prod-down_binary64_839
25×pow-to-exp_binary64_829
18×cbrt-unprod_binary64_793
17×pow1_binary64_821
15×cbrt-undiv_binary64_794
11×unswap-sqr_binary64_728 associate-*l*_binary64_701
8×div-inv_binary64_757
7×pow-prod-down_binary64_831
4×add-log-exp_binary64_799
3×*-commutative_binary64_691
1×rem-sqrt-square_binary64_773 associate-*l/_binary64_703 sqrt-pow1_binary64_778 frac-times_binary64_770 associate-*r/_binary64_702 pow1/2_binary64_840
Counts
4 → 375
Calls

4 calls:

92.0ms
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
1.0ms
(sqrt.f64 PI.f64)

series831.0ms (7.1%)

Counts
4 → 10
Calls

4 calls:

750.0ms
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
41.0ms
(*.f64 (*.f64 2 PI.f64) n)
39.0ms
(*.f64 (*.f64 2 PI.f64) n)
0.0ms
(sqrt.f64 PI.f64)

simplify158.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
385 → 385
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0527917622

prune980.0ms (8.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New3841385
Fresh156
Picked011
Done022
Total3859394

Merged error: 0b

Counts
394 → 9
Compiler

Compiled 16092 to 9572 computations (40.5% saved)

regimes444.0ms (3.8%)

Compiler

Compiled 5922 to 4810 computations (18.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01531
11531

end0.0ms (0%)

sample3.8s (32.2%)

Algorithm
1×intervals
Results
916.0ms8000×body128valid
611.0ms1348×body1024nan
314.0ms2289×body128overflowed
207.0ms674×body512nan
62.0ms996×body128nan
57.0ms329×body256nan
22.0ms233×body128invalid
Compiler

Compiled 1505 to 1224 computations (18.7% saved)

Profiling

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