Details

analyze165.0ms (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 43 to 28 computations (34.9% saved)

sample1.8s (38.6%)

Results

1.0s	6726×	body	128	valid
355.0ms	660×	body	1024	valid
199.0ms	501×	body	512	valid
93.0ms	323×	body	256	valid
34.0ms	46×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
245×	`+-commutative_binary64`
193×	`associate-+l+_binary64`
184×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	112	37
3	520	37
4	2735	37
5	4514	37

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

11.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

Compiler

Compiled 116 to 69 computations (40.5% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
✓	0.3b	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

series209.0ms (4.6%)

Counts

3 → 108

Calls

3 calls:

124.0ms

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

54.0ms

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))

30.0ms

(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))

rewrite38.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

180×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`
167×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	349	65

Stop Event

1×	node limit

Counts

3 → 89

Calls

3 calls:

36.0ms

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))

36.0ms

(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))

36.0ms

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

simplify119.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-/l*_binary64`
365×	`+-commutative_binary64`
282×	`associate-+r+_binary64`
265×	`fma-def_binary64`
218×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	883	10939
1	3352	10904

Stop Event

1×	node limit

Counts

197 → 218

prune319.0ms (6.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	216	3	219

Error

0.1b

Counts

219 → 3

Alt Table

Status	Error	Program
✓	11.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
▶	11.5b	(/.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
	50.3b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 15207 to 9490 computations (37.6% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))
	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
✓	0.3b	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
✓	0.3b	(log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))

series347.0ms (7.6%)

Counts

3 → 108

Calls

3 calls:

143.0ms

(log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))

137.0ms

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

61.0ms

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
192×	`add-cbrt-cube_binary64`
188×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	85
1	397	85

Stop Event

1×	node limit

Counts

3 → 68

Calls

3 calls:

47.0ms

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))

47.0ms

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

47.0ms

(log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))

simplify192.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-def_binary64`
704×	`associate-/l*_binary64`
302×	`+-commutative_binary64`
241×	`associate-+r+_binary64`
200×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	756	14350
1	2864	13907

Stop Event

1×	node limit

Counts

176 → 139

prune370.0ms (8.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	217	3	220

Error

0.1b

Counts

220 → 3

Alt Table

Status	Error	Program
✓	11.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
✓	11.5b	(/.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
▶	50.3b	(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)

Compiler

Compiled 15277 to 9712 computations (36.4% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha)

series17.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

17.0ms

(/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha)

rewrite41.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

831×	`log1p-expm1-u_binary64`
831×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`
85×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	185	12
2	2205	12

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

40.0ms

(/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha)

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

187×	`fma-def_binary64`
30×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
20×	`distribute-rgt-in_binary64`
18×	`associate-/r/_binary64`

Iterations

Useful iterations: 13 (0.0ms)

Iter	Nodes	Cost
0	25	646
1	51	644
2	87	584
3	113	584
4	130	554
5	158	494
6	192	494
7	257	494
8	311	494
9	324	494
10	345	494
11	368	494
12	391	494
13	410	404
14	435	404
15	453	404
16	455	404
17	456	404

Stop Event

1×

saturated

Counts

69 → 43

prune25.0ms (0.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	43	3	46

Error

0.1b

Counts

46 → 3

Alt Table

Status	Error	Program
✓	11.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
✓	11.5b	(/.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
✓	50.3b	(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)

Compiler

Compiled 764 to 573 computations (25% saved)

regimes685.0ms (14.9%)

Accuracy

Total 1.6b remaining (88.3%)

Threshold costs 0b (0%)

Counts

59 → 2

Compiler

Compiled 11472 to 7940 computations (30.8% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	94
1	42	94
2	45	94
3	47	94
4	48	94

Stop Event

1×

saturated

end89.0ms (1.9%)

Compiler: Compiled 210 to 130 computations (38.1% saved)

Iter	Nodes	Cost
0	25	646
1	51	644
2	87	584
3	113	584
4	130	554
5	158	494
6	192	494
7	257	494
8	311	494
9	324	494
10	345	494
11	368	494
12	391	494
13	410	404
14	435	404
15	453	404
16	455	404
17	456	404

Iter	Nodes	Cost
0	25	646
1	51	644
2	87	584
3	113	584
4	130	554
5	158	494
6	192	494
7	257	494
8	311	494
9	324	494
10	345	494
11	368	494
12	391	494
13	410	404
14	435	404
15	453	404
16	455	404
17	456	404

Details

analyze165.0ms (3.6%)

sample1.8s (38.6%)

simplify25.0ms (0.5%)

prune4.0ms (0.1%)

localize15.0ms (0.3%)

series209.0ms (4.6%)

rewrite38.0ms (0.8%)

simplify119.0ms (2.6%)

prune319.0ms (6.9%)

localize19.0ms (0.4%)

series347.0ms (7.6%)

rewrite49.0ms (1.1%)

simplify192.0ms (4.2%)

prune370.0ms (8.1%)

localize10.0ms (0.2%)

series17.0ms (0.4%)

rewrite41.0ms (0.9%)

simplify76.0ms (1.7%)

prune25.0ms (0.5%)

regimes685.0ms (14.9%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end89.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	25	646
1	51	644
2	87	584
3	113	584
4	130	554
5	158	494
6	192	494
7	257	494
8	311	494
9	324	494
10	345	494
11	368	494
12	391	494
13	410	404
14	435	404
15	453	404
16	455	404
17	456	404