Details

analyze481.0ms (9.9%)

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)

sample49.0ms (1%)

Algorithm

1×

intervals

Results

12.0ms	192×	body	128	valid
6.0ms	256×	pre	128	true
6.0ms	21×	body	2048	valid
5.0ms	15×	body	4096	valid
4.0ms	17×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify28.0ms (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

38.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	38.8b	(.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)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite85.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

38.5b

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:

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

Compiler

Compiled 1329 to 472 computations (64.5% saved)

series107.0ms (2.2%)

Error

0.4b

Counts

4 → 53

Calls

4 calls:

25.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
18.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1888 to 1553 computations (17.7% saved)

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

632×	`associate-r_binary64`
599×	`associate-l_binary64`
356×	`times-frac_binary64`
265×	`associate-/l*_binary64`
172×	`associate-/r*_binary64`

Counts

109 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	1921
1	422	1846
2	1167	1802
3	5015	1802

prune34.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	6	67

Error

0.4b

Counts

67 → 6

Alt Table

Status	Error	Program
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	30.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	40.1b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	46.8b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
▶	29.4b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))

Compiler

Compiled 1044 to 656 computations (37.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))
0.1b	(sqrt.f64 (/.f64 1 im))
0.2b	(*.f64 re (sqrt.f64 (/.f64 1 im)))
0.4b	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))

rewrite93.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

40×	`add-sqr-sqrt_binary64`
33×	`sqrt-prod_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
22×	`times-frac_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(*.f64 re (sqrt.f64 (/.f64 1 im)))
6.0ms	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))
3.0ms	(-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))
2.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 2298 to 1720 computations (25.2% saved)

series67.0ms (1.4%)

Error

0.4b

Counts

4 → 27

Calls

4 calls:

26.0ms	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))
19.0ms	(-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))
14.0ms	(*.f64 re (sqrt.f64 (/.f64 1 im)))
6.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 970 to 808 computations (16.7% saved)

simplify104.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

328×	`distribute-rgt-neg-in_binary64`
299×	`distribute-lft-neg-in_binary64`
292×	`unsub-neg_binary64`
284×	`*-commutative_binary64`
272×	`neg-sub0_binary64`

Counts

130 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	2122
1	297	1952
2	940	1949
3	1955	1949
4	4270	1949
5	5005	1949

prune41.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Error

0.4b

Counts

79 → 7

Alt Table

Status	Error	Program
▶	29.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))) (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))))) (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))))
✓	29.4b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	30.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	40.1b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	46.8b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 1424 to 1056 computations (25.8% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))) (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im)))))))
4.4b	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))
4.4b	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))))
4.4b	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))))

rewrite121.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))) (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im)))))))
3.0ms	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))))
3.0ms	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))))
3.0ms	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))

Compiler

Compiled 5023 to 3615 computations (28% saved)

series143.0ms (3%)

Error

0.4b

Counts

4 → 32

Calls

4 calls:

31.0ms	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))
30.0ms	(.f64 (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))) (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (*.f64 re (sqrt.f64 (/.f64 1 im)))))))
29.0ms	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))))
29.0ms	(cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im))))))

Compiler

Compiled 3832 to 3089 computations (19.4% saved)

simplify142.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

344×	`distribute-rgt-neg-in_binary64`
335×	`distribute-lft-neg-in_binary64`
285×	`exp-sum_binary64`
255×	`*-commutative_binary64`
236×	`cancel-sign-sub-inv_binary64`

Counts

119 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	167	4209
1	357	4013
2	981	3553
3	2157	3406
4	4688	3252
5	5024	3252

prune79.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	100	7	107

Error

0.4b

Counts

107 → 7

Alt Table

Status	Error	Program
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	32.0b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 re (.f64 1/2 (sqrt.f64 (/.f64 1 im)))))) 6) 1/3)) (cbrt.f64 (-.f64 (sqrt.f64 im) (.f64 (*.f64 re (sqrt.f64 (/.f64 1 im))) 1/2)))))
▶	30.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	40.1b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	46.8b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
✓	29.4b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))

Compiler

Compiled 3771 to 2773 computations (26.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
0.2b	(.f64 1/2 (/.f64 (.f64 re re) im))
9.3b	(/.f64 (*.f64 re re) im)
9.7b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))

rewrite72.0ms (1.5%)

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)
3.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1853 to 1014 computations (45.3% saved)

series87.0ms (1.8%)

Error

0.4b

Counts

4 → 40

Calls

4 calls:

28.0ms	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
23.0ms	(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))
14.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1404 to 1142 computations (18.7% saved)

simplify107.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

463×	`times-frac_binary64`
450×	`associate-/l*_binary64`
386×	`associate-*l/_binary64`
351×	`associate-*r/_binary64`
274×	`distribute-lft-in_binary64`

Counts

120 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	1986
1	387	1818
2	1205	1773
3	4743	1773
4	4994	1773
5	4947	1773

prune33.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	77	6	83

Error

0.4b

Counts

83 → 6

Alt Table

Status	Error	Program
	29.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))
	49.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	40.1b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	46.8b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 im (sqrt.f64 2))) (sqrt.f64 (/.f64 1 re))))
	29.4b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (.f64 re (sqrt.f64 (/.f64 1 im))) 1/2))))

Compiler

Compiled 1038 to 652 computations (37.2% saved)

regimes1.3s (27.5%)

Accuracy

Total 14.8b remaining (97.3%)

Threshold costs 0b (0%)

Compiler

Compiled 14277 to 9928 computations (30.5% saved)

bsearch78.0ms (1.6%)

Steps

Iters	Range		Point
6	9.326962714960999e+67	8.492472437276741e+68	9.463404869897915e+67
9	-6.081011654100943e-145	-2.2971540074850343e-150	-2.318656067702442e-150
8	-1.0663170036664903e+81	-2.981403803865652e+76	-1.0383523502862224e+81
9	-3.7342577632651844e+132	-3.9678514308931613e+126	-4.020338852037762e+126

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
6×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	117
1	77	117
2	81	117
3	82	117
4	81	117

end1.0ms (0%)

Compiler: Compiled 79 to 59 computations (25.3% saved)

sample1.4s (29.7%)

Algorithm

1×

intervals

Results

362.0ms	6051×	body	128	valid
211.0ms	679×	body	2048	valid
178.0ms	503×	body	4096	valid
112.0ms	8000×	pre	128	true
96.0ms	416×	body	1024	valid
38.0ms	231×	body	512	valid
13.0ms	120×	body	256	valid

Compiler

Compiled 201 to 153 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

analyze481.0ms (9.9%)

sample49.0ms (1%)

simplify28.0ms (0.6%)

prune1.0ms (0%)

localize11.0ms (0.2%)

rewrite85.0ms (1.8%)

series107.0ms (2.2%)

simplify61.0ms (1.3%)

prune34.0ms (0.7%)

localize10.0ms (0.2%)

rewrite93.0ms (1.9%)

series67.0ms (1.4%)

simplify104.0ms (2.2%)

prune41.0ms (0.8%)

localize20.0ms (0.4%)

rewrite121.0ms (2.5%)

series143.0ms (3%)

simplify142.0ms (2.9%)

prune79.0ms (1.6%)

localize10.0ms (0.2%)

rewrite72.0ms (1.5%)

series87.0ms (1.8%)

simplify107.0ms (2.2%)

prune33.0ms (0.7%)

regimes1.3s (27.5%)

bsearch78.0ms (1.6%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.4s (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