Details

analyze328.0ms (6.3%)

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)

sample35.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	193×	body	128	valid
6.0ms	22×	body	4096	valid
3.0ms	15×	body	2048	valid
3.0ms	256×	pre	128	true
2.0ms	14×	body	1024	valid
1.0ms	9×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify108.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	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

Error

39.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize14.0ms (0.3%)

Local error

Found 6 expressions with local error:

31.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100`
7×	`*-un-lft-identity_binary64_78` `pow1_binary64_139`
5×	`sqrt-prod_binary64_94` `add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
4×	`sqrt-div_binary64_95`
3×	`add-cbrt-cube_binary64_114` `sqrt-pow1_binary64_96` `add-exp-log_binary64_116` `cancel-sign-sub-inv_binary64_44`
2×	`flip3--_binary64_82` `flip--_binary64_53` `difference-of-squares_binary64_47` `associate-*r/_binary64_20` `pow1/2_binary64_158`
1×	`flip-+_binary64_52` `rem-sqrt-square_binary64_91` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `pow-prod-down_binary64_149` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

3 → 45

Calls

6 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

series291.0ms (5.5%)

Counts

3 → 42

Calls

3 calls:

106.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
103.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
82.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1104 to 998 computations (9.6% saved)

simplify110.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4916	1522
1	4916	1522

prune142.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Error

0.4b

Counts

88 → 8

Compiler

Compiled 1762 to 908 computations (48.5% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune7.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

0.4b

Counts

8 → 8

Compiler

Compiled 118 to 94 computations (20.3% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.1b	(sqrt.f64 (/.f64 1 im))
0.0b	(.f64 1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))
0.0b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))
0.1b	(sqrt.f64 (/.f64 1 im))
0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.4b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_100`
40×	`sqrt-prod_binary64_94`
28×	`associate-r_binary64_18`
27×	`*-un-lft-identity_binary64_78`
26×	`add-cube-cbrt_binary64_113`
20×	`times-frac_binary64_84`
17×	`pow1_binary64_139`
13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`associate-l_binary64_19`
7×	`pow-prod-down_binary64_149`
6×	`unswap-sqr_binary64_46`
5×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127`
4×	`add-log-exp_binary64_117`
3×	`*-commutative_binary64_9` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`
2×	`div-inv_binary64_75` `sqrt-div_binary64_95`
1×	`inv-pow_binary64_163` `sqrt-unprod_binary64_98` `pow-flip_binary64_152` `associate-*r/_binary64_20`

Counts

4 → 112

Calls

8 calls:

11.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
5.0ms	(*.f64 re (sqrt.f64 2))
3.0ms	(sqrt.f64 (/.f64 1 im))
0.0ms	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))

series157.0ms (3%)

Counts

4 → 15

Calls

4 calls:

92.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
29.0ms	(*.f64 re (sqrt.f64 2))
22.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
14.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 640 to 597 computations (6.7% saved)

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5027	1398

prune180.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	127	8	135

Error

0.4b

Counts

135 → 8

Compiler

Compiled 3027 to 2380 computations (21.4% saved)

localize16.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 im))
0.0b	(.f64 1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))
0.0b	(log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im)))
0.0b	(-.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)))) (.f64 1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))
0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.4b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
4.9b	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_100`
28×	`associate-r_binary64_18`
27×	`sqrt-prod_binary64_94`
20×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`associate-l_binary64_19` `pow-prod-down_binary64_149`
9×	`times-frac_binary64_84`
7×	`exp-prod_binary64_130`
6×	`unswap-sqr_binary64_46`
5×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
4×	`add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `log-pow_binary64_167` `pow1/2_binary64_158`
3×	`*-commutative_binary64_9`
1×	`exp-sum_binary64_124` `rem-exp-log_binary64_118` `sqrt-unprod_binary64_98` `div-inv_binary64_75` `log-prod_binary64_164` `sqrt-div_binary64_95` `associate-*r/_binary64_20`

Counts

4 → 100

Calls

8 calls:

14.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
6.0ms	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))
5.0ms	(*.f64 re (sqrt.f64 2))
0.0ms	(-.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)))) (.f64 1/2 (.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))))

series187.0ms (3.6%)

Counts

4 → 15

Calls

4 calls:

101.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
34.0ms	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))
30.0ms	(*.f64 re (sqrt.f64 2))
21.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

Compiler

Compiled 728 to 682 computations (6.3% saved)

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5157	1285

prune163.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	115	8	123

Error

0.4b

Counts

123 → 8

Compiler

Compiled 2838 to 2289 computations (19.3% saved)

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	374	915
1	374	915

regimes494.0ms (9.4%)

Compiler: Compiled 2136 to 1679 computations (21.4% saved)

bsearch127.0ms (2.4%)

Steps

Iters	Range		Point
5	1.4997115579960871e+91	4.4169498983791226e+91	2.6425163668929388e+91
10	2.18280916713774e+20	7.390727970954304e+35	5.594187968714849e+35
8	4.962169800219719e-24	2.4511412872876517e-20	8.443019886679552e-21
8	-3.3893284954853406e-130	-7.828998547410895e-133	-1.704786349615486e-131
9	-2.1582259929573573e+123	-4.908557165745598e+114	-3.695071676918518e+120

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes193.0ms (3.7%)

Compiler: Compiled 540 to 496 computations (8.1% saved)

bsearch61.0ms (1.2%)

Steps

Iters

Range

Point

1.4997115579960871e+91

4.4169498983791226e+91

1.5189952251471227e+91

-3.3893284954853406e-130

-7.828998547410895e-133

-7.949631741057429e-133

-2.1582259929573573e+123

-4.908557165745598e+114

-6.749403418164483e+115

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes98.0ms (1.9%)

Compiler: Compiled 326 to 336 computations (-3.1% saved)

bsearch40.0ms (0.8%)

Steps

Iters	Range		Point
5	1.4997115579960871e+91	4.4169498983791226e+91	1.5189952251471227e+91
9	-5.682409439204043e+131	-2.1582259929573573e+123	-2.194337097190631e+123

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes54.0ms (1%)

Compiler: Compiled 86 to 106 computations (-23.3% saved)

bsearch62.0ms (1.2%)

Steps

Iters	Range		Point
9	1.0347933763407709e+184	2.124919778272519e+190	1.0870141299270512e+184
9	-5.682409439204043e+131	-2.1582259929573573e+123	-2.194337097190631e+123

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes43.0ms (0.8%)

Compiler: Compiled 70 to 90 computations (-28.6% saved)

bsearch51.0ms (1%)

Steps

Iters	Range		Point
8	2.124919778272519e+190	7.860359008166931e+192	2.6890995397918132e+190
7	-3.0906155895615374e+86	-7.445785487205103e+84	-7.5266266125105474e+84

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes31.0ms (0.6%)

Compiler: Compiled 22 to 40 computations (-81.8% saved)

bsearch36.0ms (0.7%)

Steps

Iters	Range		Point
8	2.124919778272519e+190	7.860359008166931e+192	2.2140007932492494e+190

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes26.0ms (0.5%)

Accuracy

Total 13.7b remaining (97.5%)

Threshold costs 0b (0%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch41.0ms (0.8%)

Steps

Iters	Range		Point
9	9.555353633117625e-174	2.020083629670477e-167	4.8736104130745854e-170

Compiler

Compiled 259 to 215 computations (17% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	367
1	129	367

end0.0ms (0%)

sample1.8s (34.6%)

Algorithm

1×

intervals

Results

282.0ms	6105×	body	128	valid
150.0ms	636×	body	2048	valid
140.0ms	513×	body	4096	valid
110.0ms	8000×	pre	128	true
73.0ms	396×	body	1024	valid
29.0ms	222×	body	512	valid
11.0ms	128×	body	256	valid

Compiler

Compiled 850 to 685 computations (19.4% saved)

Pareto

0.4557209868273831

Details

analyze328.0ms (6.3%)

sample35.0ms (0.7%)

simplify108.0ms (2.1%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

rewrite26.0ms (0.5%)

series291.0ms (5.5%)

simplify110.0ms (2.1%)

prune142.0ms (2.7%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

rewrite40.0ms (0.8%)

series157.0ms (3%)

simplify92.0ms (1.7%)

prune180.0ms (3.4%)

localize16.0ms (0.3%)

rewrite42.0ms (0.8%)

series187.0ms (3.6%)

simplify84.0ms (1.6%)

prune163.0ms (3.1%)

simplify17.0ms (0.3%)

regimes494.0ms (9.4%)

bsearch127.0ms (2.4%)

regimes193.0ms (3.7%)

bsearch61.0ms (1.2%)

regimes98.0ms (1.9%)

bsearch40.0ms (0.8%)

regimes54.0ms (1%)

bsearch62.0ms (1.2%)

regimes43.0ms (0.8%)

bsearch51.0ms (1%)

regimes31.0ms (0.6%)

bsearch36.0ms (0.7%)

regimes26.0ms (0.5%)

bsearch41.0ms (0.8%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.8s (34.6%)

Profiling