Details

analyze419.0ms (5.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 29 to 21 computations (27.6% saved)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
1.0ms	14×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify257.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5740	19

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.3b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
26.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_83`
22×	`log-pow_binary64_163`
21×	`pow1_binary64_135`
17×	`add-sqr-sqrt_binary64_98`
16×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`sqrt-pow1_binary64_94` `associate-/l*_binary64_24` `pow1/2_binary64_154`
5×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113`
4×	`associate-/r*_binary64_23` `sqrt-div_binary64_93`
3×	`sqrt-prod_binary64_92` `flip-+_binary64_51` `flip3-+_binary64_80`
2×	`div-sub_binary64_82` `log-div_binary64_161`
1×	`rem-sqrt-square_binary64_90` `cbrt-undiv_binary64_108` `+-commutative_binary64_9` `div-exp_binary64_125` `clear-num_binary64_76` `frac-2neg_binary64_88` `sum-log_binary64_165` `div-inv_binary64_74`

Counts

3 → 74

Calls

3 calls:

9.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series275.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

187.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
41.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5721	1833

prune95.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	72	13	85

Merged error: 6.7b

Counts

85 → 13

Compiler

Compiled 1776 to 454 computations (74.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
27.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_83`
72×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
47×	`pow1_binary64_135`
43×	`log-pow_binary64_163`
24×	`associate-/r*_binary64_23`
12×	`add-exp-log_binary64_112`
11×	`add-cbrt-cube_binary64_110`
7×	`associate-/l*_binary64_24`
6×	`add-log-exp_binary64_113` `div-inv_binary64_74`
4×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
3×	`log-prod_binary64_160`
2×	`flip-+_binary64_51` `flip3-+_binary64_80` `log-div_binary64_161` `clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`rem-log-exp_binary64_115` `+-commutative_binary64_9` `associate-/r/_binary64_25` `sum-log_binary64_165`

Counts

4 → 159

Calls

4 calls:

8.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
6.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series531.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

227.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
209.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
58.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
37.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5984	4862

prune174.0ms (2.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	169	15	184

Merged error: 6.6b

Counts

184 → 15

Compiler

Compiled 4092 to 1126 computations (72.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/2 (.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
0.3b	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.4b	(.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
27.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64_112`
32×	`add-sqr-sqrt_binary64_98`
29×	`times-frac_binary64_83`
26×	`*-un-lft-identity_binary64_77`
25×	`add-cube-cbrt_binary64_109`
20×	`add-cbrt-cube_binary64_110`
16×	`pow1_binary64_135` `associate-r_binary64_19`
11×	`div-exp_binary64_125`
9×	`log-pow_binary64_163`
8×	`prod-exp_binary64_123`
6×	`cbrt-undiv_binary64_108` `associate-/l*_binary64_24`
5×	`associate-/r*_binary64_23`
4×	`associate-l_binary64_20` `add-log-exp_binary64_113` `cbrt-unprod_binary64_107`
3×	`log-prod_binary64_160` `1-exp_binary64_118` `rec-exp_binary64_124` `unswap-sqr_binary64_45` `div-inv_binary64_74`
2×	`associate-*r/_binary64_21` `associate-/r/_binary64_25` `log-div_binary64_161` `clear-num_binary64_76` `un-div-inv_binary64_75` `frac-2neg_binary64_88`
1×	`rem-log-exp_binary64_115` `pow-prod-down_binary64_145` `flip-+_binary64_51` `flip3-+_binary64_80` `inv-pow_binary64_159` `*-commutative_binary64_10` `pow-flip_binary64_148`

Counts

4 → 116

Calls

4 calls:

9.0ms	(.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.0ms	(/.f64 1/2 (.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
5.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series604.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
210.0ms	(/.f64 1/2 (.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
117.0ms	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
64.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5369	2440

prune123.0ms (1.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	127	16	143

Merged error: 6.6b

Counts

143 → 16

Compiler

Compiled 2705 to 1008 computations (62.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.3b	(/.f64 1/2 (log.f64 base))
0.3b	(/.f64 (/.f64 1/2 (log.f64 base)) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
27.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite89.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

688×	`times-frac_binary64_83`
295×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
116×	`pow1_binary64_135`
111×	`log-pow_binary64_163`
37×	`div-inv_binary64_74`
33×	`add-exp-log_binary64_112`
24×	`associate-/r*_binary64_23`
22×	`associate-/l*_binary64_24`
20×	`add-cbrt-cube_binary64_110`
19×	`div-exp_binary64_125`
10×	`cbrt-undiv_binary64_108`
4×	`add-log-exp_binary64_113`
3×	`log-prod_binary64_160` `1-exp_binary64_118` `rec-exp_binary64_124` `clear-num_binary64_76` `frac-2neg_binary64_88`
2×	`log-div_binary64_161`
1×	`rem-log-exp_binary64_115` `flip-+_binary64_51` `flip3-+_binary64_80` `inv-pow_binary64_159` `associate-/r/_binary64_25` `associate-/l/_binary64_26` `pow-flip_binary64_148`

Counts

4 → 392

Calls

4 calls:

15.0ms	(/.f64 (/.f64 1/2 (log.f64 base)) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
5.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
3.0ms	(/.f64 1/2 (log.f64 base))

series570.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (/.f64 1/2 (log.f64 base)) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
175.0ms	(/.f64 1/2 (log.f64 base))
126.0ms	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
58.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify185.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

404 → 404

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4981	14899
1	4981	14899

prune464.0ms (6.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	401	3	404
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	404	16	420

Merged error: 6.6b

Counts

420 → 16

Compiler

Compiled 10887 to 3953 computations (63.7% saved)

regimes705.0ms (10%)

Compiler: Compiled 4951 to 3591 computations (27.5% saved)

bsearch88.0ms (1.2%)

Steps

Iters	Range		Point
8	2.0355860987462653e+130	2.2371059522363548e+133	8.138679595525005e+130
6	-4.15452649581536e+72	-5.971042625070159e+71	-1.4606828681743375e+72

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	57
1	30	57

end0.0ms (0%)

sample2.0s (28.9%)

Algorithm

1×

intervals

Results

787.0ms	8000×	body	128	valid
96.0ms	1017×	body	128	nan

Compiler

Compiled 1043 to 756 computations (27.5% saved)

Details

analyze419.0ms (5.9%)

sample36.0ms (0.5%)

simplify257.0ms (3.6%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

rewrite25.0ms (0.3%)

series275.0ms (3.9%)

simplify79.0ms (1.1%)

prune95.0ms (1.3%)

localize11.0ms (0.2%)

rewrite40.0ms (0.6%)

series531.0ms (7.5%)

simplify99.0ms (1.4%)

prune174.0ms (2.5%)

localize12.0ms (0.2%)

rewrite36.0ms (0.5%)

series604.0ms (8.6%)

simplify71.0ms (1%)

prune123.0ms (1.7%)

localize13.0ms (0.2%)

rewrite89.0ms (1.3%)

series570.0ms (8.1%)

simplify185.0ms (2.6%)

prune464.0ms (6.6%)

regimes705.0ms (10%)

bsearch88.0ms (1.2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (28.9%)

Profiling