Details

analyze368.0ms (8.4%)

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)

sample36.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	192×	body	128	valid
6.0ms	28×	body	2048	valid
5.0ms	17×	body	4096	valid
3.0ms	256×	pre	128	true
2.0ms	12×	body	1024	valid
1.0ms	4×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify27.0ms (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

prune2.0ms (0.1%)

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

37.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	37.7b	(.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)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.1b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite113.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

37.5b

Rules

11×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
8×	`pow1_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 56

Calls

4 calls:

8.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1329 to 472 computations (64.5% saved)

series140.0ms (3.2%)

Error

0.4b

Counts

4 → 52

Calls

4 calls:

34.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
26.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
24.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1780 to 1457 computations (18.1% saved)

simplify119.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-r_binary64`
567×	`associate-l_binary64`
350×	`times-frac_binary64`
236×	`associate-/l*_binary64`
161×	`associate-/r*_binary64`

Counts

108 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	1860
1	401	1785
2	1076	1770
3	4677	1767
4	4998	1767
5	4936	1767

prune50.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Error

11.0b

Counts

64 → 6

Alt Table

Status	Error	Program
	43.0b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	38.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re))))
	43.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
▶	36.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))

Compiler

Compiled 1012 to 603 computations (40.4% saved)

localize13.0ms (0.3%)

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)
7.4b	(/.f64 (*.f64 re re) im)
11.5b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))

rewrite122.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

9.0b

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:

8.0ms	(.f64 1/2 (/.f64 (.f64 re re) im))
7.0ms	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
7.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
5.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1853 to 1014 computations (45.3% saved)

series115.0ms (2.6%)

Error

8.9b

Counts

4 → 40

Calls

4 calls:

37.0ms	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
31.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
19.0ms	(.f64 1/2 (/.f64 (.f64 re re) im))
17.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1404 to 1142 computations (18.7% saved)

simplify97.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
457×	`associate-/l*_binary64`
395×	`associate-*l/_binary64`
353×	`associate-*r/_binary64`
273×	`distribute-lft-in_binary64`

Counts

120 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	1986
1	389	1818
2	1206	1793
3	4757	1793
4	4954	1793

prune49.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Error

8.8b

Counts

83 → 6

Alt Table

Status	Error	Program
	43.0b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	43.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
▶	34.0b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	34.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))

Compiler

Compiled 1145 to 729 computations (36.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

8.8b

Rules

15×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 31

Calls

1 calls:

7.0ms

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

Compiler

Compiled 294 to 220 computations (25.2% saved)

series7.0ms (0.2%)

Error

8.8b

Counts

1 → 3

Calls

1 calls:

7.0ms

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

Compiler

Compiled 81 to 73 computations (9.9% saved)

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

564×	`log-div_binary64`
359×	`associate-l_binary64`
346×	`log-prod_binary64`
296×	`associate-*l/_binary64`
288×	`unswap-sqr_binary64`

Counts

34 → 13

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	367
1	83	361
2	199	361
3	249	361
4	342	361
5	528	361
6	1013	361
7	2695	361
8	4284	361
9	4989	361
10	4907	361

prune24.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	10	9	19

Error

8.8b

Counts

19 → 9

Alt Table

Status	Error	Program
	43.0b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	43.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
▶	33.8b	(.f64 1/2 (sqrt.f64 (.f64 im 2)))
	34.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))
	34.2b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (cbrt.f64 im))) (sqrt.f64 (cbrt.f64 im))))
	41.2b	(.f64 1/2 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) 3)))
	34.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 371 to 292 computations (21.3% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

8.8b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 8.8b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune8.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

8.8b

Counts

9 → 9

Alt Table

Status	Error	Program
	43.0b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	43.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	33.8b	(.f64 1/2 (sqrt.f64 (.f64 im 2)))
	34.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))
	34.2b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (cbrt.f64 im))) (sqrt.f64 (cbrt.f64 im))))
	41.2b	(.f64 1/2 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) 3)))
	34.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 133 to 102 computations (23.3% saved)

regimes1.6s (35.8%)

Accuracy

Total 6.2b remaining (46.9%)

Threshold costs 0b (0%)

Compiler

Compiled 15888 to 10722 computations (32.5% saved)

bsearch64.0ms (1.5%)

Steps

Iters	Range		Point
10	5.904877514885216e-11	2253.484662889386	1.9790760428740222e-07
9	-5.602059868838172e-159	-8.408061398285703e-164	-8.516731262603456e-164
7	-3.3004671234819746e+99	-8.138393195474647e+97	-1.267084959064262e+99

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	99
1	65	99
2	70	99
3	72	99
4	73	99
5	72	99

end2.0ms (0%)

Compiler: Compiled 67 to 51 computations (23.9% saved)

sample1.3s (29.7%)

Algorithm

1×

intervals

Results

290.0ms	6077×	body	128	valid
156.0ms	668×	body	2048	valid
142.0ms	509×	body	4096	valid
90.0ms	8000×	pre	128	true
70.0ms	407×	body	1024	valid
28.0ms	217×	body	512	valid
11.0ms	122×	body	256	valid

Compiler

Compiled 222 to 169 computations (23.9% 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

analyze368.0ms (8.4%)

sample36.0ms (0.8%)

simplify27.0ms (0.6%)

prune2.0ms (0.1%)

localize13.0ms (0.3%)

rewrite113.0ms (2.6%)

series140.0ms (3.2%)

simplify119.0ms (2.7%)

prune50.0ms (1.1%)

localize13.0ms (0.3%)

rewrite122.0ms (2.8%)

series115.0ms (2.6%)

simplify97.0ms (2.2%)

prune49.0ms (1.1%)

localize5.0ms (0.1%)

rewrite33.0ms (0.7%)

series7.0ms (0.2%)

simplify91.0ms (2.1%)

prune24.0ms (0.6%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.2%)

prune8.0ms (0.2%)

regimes1.6s (35.8%)

bsearch64.0ms (1.5%)

simplify6.0ms (0.1%)

end2.0ms (0%)

sample1.3s (29.7%)

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