Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample2.3s (80.5%)

Results

1.3s	2697×	body	1024	valid
456.0ms	1381×	body	512	valid
281.0ms	3193×	body	128	valid
110.0ms	709×	body	256	valid
104.0ms	276×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

95×	`fma-def_binary64`
80×	`fma-neg_binary64`
32×	`distribute-rgt-in_binary64`
27×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 21 to 13 computations (38.1% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (expm1.f64 x) x)

rewrite79.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

768×	`log1p-udef_binary64`
417×	`log1p-expm1-u_binary64`
417×	`expm1-log1p-u_binary64`
357×	`pow1_binary64`
289×	`unpow-prod-down_binary64`

Counts

1 → 61

Calls

1 calls:

78.0ms

(/.f64 (expm1.f64 x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	82	6
2	1076	6
3	4800	6
4	6280	6

simplify107.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

538×	`unswap-sqr_binary64`
529×	`associate-l_binary64`
501×	`fma-neg_binary64`
484×	`fma-def_binary64`
348×	`associate-/l*_binary64`

Counts

73 → 71

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	91
1	67	89
2	140	86
3	327	79
4	748	76
5	2248	76
6	4569	76
7	4950	76
8	5000	76
9	4913	76

prune61.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	2	72

Error

Counts

72 → 2

Alt Table

Status	Error	Program
▶	20.0b	(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
✓	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 776 to 361 computations (53.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
✓	0.0b	(fma.f64 x (fma.f64 x 1/24 1/6) 1/2)
✓	0.2b	(fma.f64 x 1/24 1/6)

series6.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

2.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
2.0ms	(fma.f64 x (fma.f64 x 1/24 1/6) 1/2)
2.0ms	(fma.f64 x 1/24 1/6)

rewrite76.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log1p-expm1-u_binary64`
723×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
85×	`fma-neg_binary64`

Counts

3 → 69

Calls

3 calls:

75.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
75.0ms	(fma.f64 x (fma.f64 x 1/24 1/6) 1/2)
75.0ms	(fma.f64 x 1/24 1/6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	178	27
2	1830	27
3	4983	27
4	4844	27

simplify74.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

538×	`unswap-sqr_binary64`
524×	`associate-l_binary64`
482×	`distribute-rgt-in_binary64`
442×	`distribute-lft-in_binary64`
437×	`fma-def_binary64`

Counts

105 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	363
1	67	341
2	128	293
3	270	264
4	565	258
5	1638	258
6	2842	258
7	3174	258
8	4987	258
9	4919	258

prune59.0ms (2.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	94	2	96

Error

Counts

96 → 2

Alt Table

Status	Error	Program
✓	20.0b	(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
✓	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 1294 to 977 computations (24.5% saved)

regimes22.0ms (0.8%)

Accuracy

Total 0.0b remaining (71.4%)

Threshold costs 0.0b (71.4%)

Counts

5 → 1

Compiler

Compiled 127 to 95 computations (25.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end38.0ms (1.3%)

Compiler: Compiled 26 to 17 computations (34.6% saved)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

Details

analyze4.0ms (0.1%)

sample2.3s (80.5%)

simplify17.0ms (0.6%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite79.0ms (2.7%)

simplify107.0ms (3.7%)

prune61.0ms (2.1%)

localize6.0ms (0.2%)

series6.0ms (0.2%)

rewrite76.0ms (2.6%)

simplify74.0ms (2.6%)

prune59.0ms (2.1%)

regimes22.0ms (0.8%)

simplify2.0ms (0.1%)

end38.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6