Details

analyze321.0ms (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample32.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	199×	body	128	valid
4.0ms	14×	body	4096	valid
4.0ms	256×	pre	128	true
3.0ms	15×	body	2048	valid
3.0ms	17×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify163.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	156	23
1	156	23

prune3.0ms (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: 36.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
27.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_435`
7×	`pow1_binary64_472`
6×	`*-un-lft-identity_binary64_414`
5×	`sqrt-prod_binary64_429` `add-log-exp_binary64_450`
4×	`sqrt-div_binary64_430` `add-cube-cbrt_binary64_446`
3×	`sqrt-pow1_binary64_431` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
2×	`flip3--_binary64_418` `difference-of-squares_binary64_383` `pow1/2_binary64_491` `flip--_binary64_389` `associate-*r/_binary64_358`
1×	`distribute-lft-out--_binary64_368` `flip3-+_binary64_417` `diff-log_binary64_503` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `flip-+_binary64_388` `rem-sqrt-square_binary64_427`

Counts

3 → 42

Calls

3 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series325.0ms (8.7%)

Counts

3 → 9

Calls

3 calls:

212.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
61.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
52.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5484	923

prune71.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 8.2b

Counts

52 → 8

Compiler

Compiled 1158 to 521 computations (55% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.2b	(sqrt.f64 (*.f64 2 (-.f64 im re)))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_472`
2×	`sqrt-div_binary64_430` `sqrt-pow1_binary64_431` `associate-*r/_binary64_358`
1×	`flip3--_binary64_418` `add-cube-cbrt_binary64_446` `sqrt-prod_binary64_429` `pow-prod-down_binary64_482` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450` `pow1/2_binary64_491` `flip--_binary64_389` `add-sqr-sqrt_binary64_435`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series114.0ms (3.1%)

Counts

1 → 3

Calls

1 calls:

114.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify47.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4965	253
1	4965	253

prune21.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	15	9	24

Merged error: 8.1b

Counts

24 → 9

Compiler

Compiled 373 to 250 computations (33% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_435`
17×	`sqrt-prod_binary64_429`
11×	`*-un-lft-identity_binary64_414`
8×	`associate-r_binary64_356`
7×	`pow1_binary64_472` `add-cube-cbrt_binary64_446`
6×	`associate-l_binary64_357`
4×	`sqrt-div_binary64_430` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `unswap-sqr_binary64_382`
3×	`sqrt-pow1_binary64_431` `pow-prod-down_binary64_482` `pow1/2_binary64_491`
2×	`flip3--_binary64_418` `distribute-lft-out--_binary64_368` `difference-of-squares_binary64_383` `add-log-exp_binary64_450` `flip--_binary64_389` `associate-*r/_binary64_358`
1×	`*-commutative_binary64_347` `prod-exp_binary64_460` `sqrt-unprod_binary64_433` `cbrt-unprod_binary64_444` `rem-sqrt-square_binary64_427`

Counts

2 → 51

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series168.0ms (4.5%)

Counts

2 → 6

Calls

2 calls:

113.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
55.0ms	(sqrt.f64 (-.f64 im re))

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4965	838
1	4965	838

prune55.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	57	9	66

Merged error: 8.1b

Counts

66 → 9

Compiler

Compiled 1011 to 609 computations (39.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (-.f64 im re)))
0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.8b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_435`
28×	`sqrt-prod_binary64_429` `log-prod_binary64_497`
23×	`*-un-lft-identity_binary64_414`
20×	`exp-sum_binary64_457`
15×	`add-cube-cbrt_binary64_446`
11×	`pow1_binary64_472` `associate-r_binary64_356`
8×	`sqrt-div_binary64_430`
6×	`log-pow_binary64_500` `log-div_binary64_498` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `associate-l_binary64_357` `unswap-sqr_binary64_382` `exp-prod_binary64_463`
4×	`flip3--_binary64_418` `distribute-lft-out--_binary64_368` `difference-of-squares_binary64_383` `exp-diff_binary64_459` `add-log-exp_binary64_450` `flip--_binary64_389`
3×	`sqrt-pow1_binary64_431` `pow1/2_binary64_491`
2×	`associate-*r/_binary64_358`
1×	`rem-log-exp_binary64_452` `*-commutative_binary64_347` `prod-exp_binary64_460` `rem-exp-log_binary64_451` `pow-prod-down_binary64_482` `cbrt-unprod_binary64_444` `rem-sqrt-square_binary64_427`

Counts

4 → 98

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
9.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
5.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series632.0ms (16.9%)

Counts

4 → 12

Calls

4 calls:

293.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
213.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
72.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
54.0ms	(sqrt.f64 (-.f64 im re))

simplify54.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5004	1612

prune93.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	110	9	119

Merged error: 8.1b

Counts

119 → 9

Compiler

Compiled 1828 to 1016 computations (44.4% saved)

regimes137.0ms (3.7%)

Compiler: Compiled 613 to 419 computations (31.6% saved)

bsearch70.0ms (1.9%)

Steps

Iters	Range		Point
6	6.886385081888518e-20	3.644294487492142e-19	6.988466119870524e-20
9	-2.7260457505491215e-65	-6.681870966069836e-71	-6.747633475511543e-71
10	-3.727438662001056e+149	-5.328097567637765e+135	-9.933850798548319e+135

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	114
1	63	114

end0.0ms (0%)

sample1.2s (31.6%)

Algorithm

1×

intervals

Results

280.0ms	6064×	body	128	valid
145.0ms	504×	body	4096	valid
139.0ms	631×	body	2048	valid
113.0ms	8000×	pre	128	true
77.0ms	440×	body	1024	valid
32.0ms	249×	body	512	valid
10.0ms	112×	body	256	valid

Compiler

Compiled 248 to 165 computations (33.5% saved)

Details

analyze321.0ms (8.6%)

sample32.0ms (0.9%)

simplify163.0ms (4.4%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

rewrite29.0ms (0.8%)

series325.0ms (8.7%)

simplify55.0ms (1.5%)

prune71.0ms (1.9%)

localize6.0ms (0.2%)

rewrite6.0ms (0.2%)

series114.0ms (3.1%)

simplify47.0ms (1.3%)

prune21.0ms (0.6%)

localize6.0ms (0.2%)

rewrite19.0ms (0.5%)

series168.0ms (4.5%)

simplify65.0ms (1.8%)

prune55.0ms (1.5%)

localize10.0ms (0.3%)

rewrite40.0ms (1.1%)

series632.0ms (16.9%)

simplify54.0ms (1.4%)

prune93.0ms (2.5%)

regimes137.0ms (3.7%)

bsearch70.0ms (1.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (31.6%)

Profiling