Details

analyze467.0ms (10.7%)

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 20 to 14 computations (30% saved)

sample42.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	213×	body	128	valid
8.0ms	16×	body	4096	valid
4.0ms	13×	body	2048	valid
4.0ms	256×	pre	128	true
1.0ms	6×	body	1024	valid
1.0ms	6×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify26.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
37×	`sub-neg_binary64`
27×	`unsub-neg_binary64`
27×	`neg-mul-1_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

37.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	37.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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)
31.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite66.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

37.4b

Rules

10×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`pow1_binary64`
5×	`sqrt-prod_binary64`
5×	`add-cube-cbrt_binary64`

Counts

3 → 45

Calls

3 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1063 to 371 computations (65.1% saved)

series78.0ms (1.8%)

Error

0.4b

Counts

3 → 36

Calls

3 calls:

24.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
16.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1376 to 1121 computations (18.5% saved)

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Rules

349×	`distribute-rgt-neg-in_binary64`
335×	`distribute-lft-neg-in_binary64`
328×	`associate-r_binary64`
309×	`associate-l_binary64`
266×	`unswap-sqr_binary64`

Counts

81 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	1369
1	306	1305
2	750	1276
3	2891	1270
4	4644	1270
5	4950	1270

prune26.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	39	6	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	7	46

Error

0.4b

Counts

46 → 7

Alt Table

Status	Error	Program
	42.1b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	52.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
▶	27.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))))
	46.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	29.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
✓	37.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 813 to 496 computations (39% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite77.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

23×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`pow1_binary64`

Counts

4 → 84

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))
6.0ms	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
3.0ms	(+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))
3.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 1892 to 1423 computations (24.8% saved)

series73.0ms (1.7%)

Error

0.4b

Counts

4 → 27

Calls

4 calls:

25.0ms	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))
24.0ms	(+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))
16.0ms	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
4.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 976 to 814 computations (16.6% saved)

simplify112.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

492×	`neg-mul-1_binary64`
449×	`*-commutative_binary64`
332×	`distribute-rgt-neg-in_binary64`
267×	`times-frac_binary64`
253×	`exp-prod_binary64`

Counts

111 → 68

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1896
1	337	1744
2	1138	1741
3	2656	1741
4	4637	1741
5	5258	1741

prune40.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	67	8	75

Error

0.4b

Counts

75 → 8

Alt Table

Status	Error	Program
	42.1b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	52.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
✓	27.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))))
	46.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	29.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
▶	27.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))))
✓	37.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 1309 to 987 computations (24.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 im))
0.3b	(*.f64 re (sqrt.f64 (/.f64 1 im)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))

rewrite116.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

50×	`sqrt-prod_binary64`
46×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
26×	`associate-r_binary64`

Counts

4 → 117

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2))))
8.0ms	(.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))
7.0ms	(*.f64 re (sqrt.f64 (/.f64 1 im)))
3.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 3082 to 2460 computations (20.2% saved)

series78.0ms (1.8%)

Error

0.4b

Counts

4 → 27

Calls

4 calls:

28.0ms	(.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))
25.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2))))
16.0ms	(*.f64 re (sqrt.f64 (/.f64 1 im)))
5.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 1175 to 1013 computations (13.8% saved)

simplify141.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

404×	`*-commutative_binary64`
347×	`distribute-rgt-in_binary64`
345×	`distribute-lft-in_binary64`
312×	`exp-prod_binary64`
239×	`associate-*l/_binary64`

Counts

144 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	2869
1	357	2501
2	1178	2461
3	2534	2461
4	4423	2461
5	4814	2461
6	4940	2461

prune49.0ms (1.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	87	8	95

Error

0.4b

Counts

95 → 8

Alt Table

Status	Error	Program
	42.1b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	52.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
✓	27.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))))
	46.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
▶	29.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
✓	27.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))))
✓	37.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 1723 to 1359 computations (21.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 1/2 (/.f64 (.f64 re re) im))
0.0b	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
7.0b	(/.f64 (*.f64 re re) im)
9.4b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))

rewrite80.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(.f64 1/2 (/.f64 (.f64 re re) im))
5.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
5.0ms	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
4.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1853 to 1014 computations (45.3% saved)

series80.0ms (1.8%)

Error

0.4b

Counts

4 → 38

Calls

4 calls:

27.0ms	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
20.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
15.0ms	(.f64 1/2 (/.f64 (.f64 re re) im))
13.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1265 to 1024 computations (19.1% saved)

simplify103.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

495×	`associate-l_binary64`
394×	`associate-/l*_binary64`
352×	`associate-*l/_binary64`
340×	`times-frac_binary64`
329×	`associate-*r/_binary64`

Counts

118 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	1857
1	339	1689
2	1044	1659
3	4598	1659
4	4942	1659
5	4961	1659

prune29.0ms (0.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	74	8	82

Error

0.4b

Counts

82 → 8

Alt Table

Status	Error	Program
	42.1b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	52.2b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
	27.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))))
	46.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	58.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	29.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	27.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (sqrt.f64 im) (.f64 -1/2 (*.f64 re (sqrt.f64 (/.f64 1 im))))) (sqrt.f64 (sqrt.f64 2)))))
	37.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 999 to 623 computations (37.6% saved)

regimes912.0ms (20.8%)

Accuracy

Total 14.9b remaining (97.1%)

Threshold costs 0b (0%)

Compiler

Compiled 9917 to 6752 computations (31.9% saved)

bsearch157.0ms (3.6%)

Steps

Iters	Range		Point
10	1.2355481294931846e+149	4.1221295121283705e+164	1.261312147033122e+149
5	4.947750256647742e+107	1.0476193200587676e+108	9.367247253923697e+107
9	3.0869078642302355e+81	1.6329201413477083e+87	5.926338806316416e+85
6	-3.629389852916924e-38	-2.6189451470092445e-39	-2.6621240162684264e-39
10	-1.2374154247336943e+157	-6.888236007840666e+140	-6.114175565259216e+149

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	125
1	83	125
2	89	125
3	91	125
4	92	125
5	91	125

end2.0ms (0%)

Compiler: Compiled 84 to 64 computations (23.8% saved)

sample1.5s (34%)

Algorithm

1×

intervals

Results

387.0ms	6070×	body	128	valid
197.0ms	540×	body	4096	valid
195.0ms	656×	body	2048	valid
113.0ms	8000×	pre	128	true
98.0ms	404×	body	1024	valid
46.0ms	230×	body	512	valid
12.0ms	100×	body	256	valid

Compiler

Compiled 244 to 188 computations (23% saved)

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

Details

analyze467.0ms (10.7%)

sample42.0ms (0.9%)

simplify26.0ms (0.6%)

prune1.0ms (0%)

localize9.0ms (0.2%)

rewrite66.0ms (1.5%)

series78.0ms (1.8%)

simplify87.0ms (2%)

prune26.0ms (0.6%)

localize10.0ms (0.2%)

rewrite77.0ms (1.8%)

series73.0ms (1.7%)

simplify112.0ms (2.6%)

prune40.0ms (0.9%)

localize13.0ms (0.3%)

rewrite116.0ms (2.7%)

series78.0ms (1.8%)

simplify141.0ms (3.2%)

prune49.0ms (1.1%)

localize10.0ms (0.2%)

rewrite80.0ms (1.8%)

series80.0ms (1.8%)

simplify103.0ms (2.4%)

prune29.0ms (0.7%)

regimes912.0ms (20.8%)

bsearch157.0ms (3.6%)

simplify7.0ms (0.2%)

end2.0ms (0%)

sample1.5s (34%)

Profiling

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23