Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
37.5%	12.5%	50%	3
43.7%	6.2%	50%	4
46.8%	3.1%	50%	5
48.4%	1.6%	50%	6
49.2%	0.8%	50%	7
49.6%	0.4%	50%	8
49.8%	0.2%	50%	9
49.9%	0.1%	50%	10
49.9%	0%	50%	11
49.9%	0%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample12.2s (90.2%)

Results

9.8s	4287×	body	2048	valid
1.7s	2128×	body	1024	valid
403.0ms	1011×	body	512	valid
152.0ms	543×	body	256	valid
42.0ms	287×	body	128	valid

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
278×	`fma-neg_binary64`
246×	`times-frac_binary64`
181×	`div-sub_binary64`
119×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	11	11
2	18	11
3	29	11
4	51	11
5	74	11
6	122	11
7	184	11
8	265	11
9	461	11
10	758	11
11	822	11
12	763	11
13	778	11
14	800	11
15	810	11
16	741	11

prune1.0ms (0%)

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

27.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.0b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
✓	2.5b	(-.f64 x (sin.f64 x))

series13.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

11.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite110.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u_binary64`
864×	`expm1-log1p-u_binary64`
591×	`prod-diff_binary64`
254×	`egg-rr`
75×	`add-sqr-sqrt_binary64`

Counts

2 → 254

Calls

2 calls:

100.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
100.0ms	(-.f64 x (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	140	17
2	2079	17
3	6446	17
0	0	0
1	0	0

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
598×	`distribute-rgt-neg-in_binary64`
542×	`sub-neg_binary64`
478×	`cancel-sign-sub-inv_binary64`
455×	`distribute-lft-neg-in_binary64`

Counts

272 → 274

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	272
1	132	266
2	331	262
3	1015	248
4	2739	248
5	4359	248
6	4736	248
7	4965	248
8	4900	248

prune143.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	271	3	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	272	3	275

Error

0.1b

Counts

275 → 3

Alt Table

Status	Error	Program
	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 8) -143/604800 (fma.f64 (pow.f64 x 6) -11/15120 (.f64 (pow.f64 x 4) -23/360))))
▶	0.2b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -23/360 1/6)))
	8.9b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/6 (pow.f64 x 3))) (tan.f64 x))

Compiler

Compiled 10437 to 2731 computations (73.8% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 x x) -23/360 1/6)
✓	0.1b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -23/360 1/6)))
✓	0.3b	(.f64 x (fma.f64 (.f64 x x) -23/360 1/6))

series9.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -23/360 1/6)))
3.0ms	(.f64 x (fma.f64 (.f64 x x) -23/360 1/6))
2.0ms	(fma.f64 (*.f64 x x) -23/360 1/6)

rewrite48.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

673×	`log1p-expm1-u_binary64`
673×	`expm1-log1p-u_binary64`
355×	`log-prod_binary64`
136×	`expm1-udef_binary64`
136×	`log1p-udef_binary64`

Counts

3 → 71

Calls

3 calls:

46.0ms	(fma.f64 (*.f64 x x) -23/360 1/6)
46.0ms	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -23/360 1/6)))
46.0ms	(.f64 x (fma.f64 (.f64 x x) -23/360 1/6))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	33
1	163	33
2	1761	33
3	5183	33
0	0	0
1	0	0

simplify145.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1048×	`fma-def_binary64`
808×	`fma-neg_binary64`
804×	`unswap-sqr_binary64`
386×	`distribute-rgt-neg-in_binary64`
348×	`distribute-lft-neg-in_binary64`

Counts

107 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	405
1	55	369
2	118	351
3	316	351
4	972	351
5	1853	351
6	4476	351
7	4753	351
8	4995	351
9	4999	351
10	4989	351
11	4999	351
12	5256	351

prune74.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Error

0.0b

Counts

89 → 5

Alt Table

Status	Error	Program
▶	0.2b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6))) 2)
	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 8) -143/604800 (fma.f64 (pow.f64 x 6) -11/15120 (.f64 (pow.f64 x 4) -23/360))))
	0.3b	(.f64 x (.f64 x (exp.f64 (log.f64 (fma.f64 (*.f64 x x) -23/360 1/6)))))
✓	0.2b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -23/360 1/6)))
	8.9b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/6 (pow.f64 x 3))) (tan.f64 x))

Compiler

Compiled 1333 to 812 computations (39.1% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (*.f64 x x) -23/360 1/6)
✓	0.0b	(.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6)))
✓	0.2b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6))) 2)

series48.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

40.0ms	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6))) 2)
8.0ms	(.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6)))

rewrite44.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

762×	`log1p-expm1-u_binary64`
762×	`expm1-log1p-u_binary64`
157×	`expm1-udef_binary64`
157×	`log1p-udef_binary64`
92×	`add-sqr-sqrt_binary64`

Counts

2 → 43

Calls

2 calls:

43.0ms	(.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6)))
43.0ms	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	205	27
2	2002	27
3	4968	27
0	0	0
1	0	0

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-neg_binary64`
753×	`fma-def_binary64`
581×	`times-frac_binary64`
493×	`cancel-sign-sub-inv_binary64`
234×	`unswap-sqr_binary64`

Counts

67 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	550
1	200	464
2	566	450
3	1952	448
4	4908	448
5	5247	448

prune80.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	103	5	108

Error

0.0b

Counts

108 → 5

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))
	0.3b	(.f64 x (.f64 x (exp.f64 (log.f64 (fma.f64 (*.f64 x x) -23/360 1/6)))))
✓	0.2b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6))) 2)
✓	0.2b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -23/360 1/6)))
	8.9b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/6 (pow.f64 x 3))) (tan.f64 x))

Compiler

Compiled 1818 to 1288 computations (29.2% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (*.f64 x x) -23/360 1/6)
✓	0.2b	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))

series4.0ms (0%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))

rewrite38.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

594×	`log1p-expm1-u_binary64`
594×	`expm1-log1p-u_binary64`
296×	`log-prod_binary64`
171×	`pow2_binary64`
120×	`pow1/3_binary64`

Counts

1 → 24

Calls

1 calls:

37.0ms

(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	144	14
2	1540	14
3	4868	14
0	0	0
1	0	0

simplify144.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1570×	`fma-def_binary64`
710×	`distribute-rgt-in_binary64`
710×	`fma-neg_binary64`
584×	`distribute-rgt-neg-in_binary64`
487×	`cancel-sign-sub-inv_binary64`

Counts

36 → 30

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	165
1	28	147
2	58	147
3	160	147
4	515	147
5	963	147
6	1784	147
7	2810	147
8	3880	147
9	4122	147
10	2794	147
11	2925	147
12	3119	147
13	4949	147
14	4751	147

prune43.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	61	5	66

Error

Counts

66 → 5

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))
✓	0.2b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 (.f64 x x) -23/360 1/6))) 2)
✓	0.2b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -23/360 1/6)))
	0.3b	(.f64 (.f64 x x) (exp.f64 (log.f64 (fma.f64 (*.f64 x x) -23/360 1/6))))
	8.9b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/6 (pow.f64 x 3))) (tan.f64 x))

Compiler

Compiled 913 to 502 computations (45% saved)

regimes88.0ms (0.7%)

Accuracy

Total 0.2b remaining (40.7%)

Threshold costs 0.2b (40.7%)

Counts

62 → 1

Compiler

Compiled 1426 to 986 computations (30.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	10	14
2	10	14

end64.0ms (0.5%)

Compiler: Compiled 83 to 55 computations (33.7% saved)

Iter	Nodes	Cost
0	6	11
1	11	11
2	18	11
3	29	11
4	51	11
5	74	11
6	122	11
7	184	11
8	265	11
9	461	11
10	758	11
11	822	11
12	763	11
13	778	11
14	800	11
15	810	11
16	741	11

Iter	Nodes	Cost
0	6	11
1	11	11
2	18	11
3	29	11
4	51	11
5	74	11
6	122	11
7	184	11
8	265	11
9	461	11
10	758	11
11	822	11
12	763	11
13	778	11
14	800	11
15	810	11
16	741	11

Details

analyze4.0ms (0%)

sample12.2s (90.2%)

simplify50.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0%)

series13.0ms (0.1%)

rewrite110.0ms (0.8%)

simplify104.0ms (0.8%)

prune143.0ms (1.1%)

localize7.0ms (0%)

series9.0ms (0.1%)

rewrite48.0ms (0.4%)

simplify145.0ms (1.1%)

prune74.0ms (0.5%)

localize6.0ms (0%)

series48.0ms (0.4%)

rewrite44.0ms (0.3%)

simplify52.0ms (0.4%)

prune80.0ms (0.6%)

localize4.0ms (0%)

series4.0ms (0%)

rewrite38.0ms (0.3%)

simplify144.0ms (1.1%)

prune43.0ms (0.3%)

regimes88.0ms (0.7%)

simplify2.0ms (0%)

end64.0ms (0.5%)

Profiling

Iter	Nodes	Cost
0	6	11
1	11	11
2	18	11
3	29	11
4	51	11
5	74	11
6	122	11
7	184	11
8	265	11
9	461	11
10	758	11
11	822	11
12	763	11
13	778	11
14	800	11
15	810	11
16	741	11