Details

analyze4.0ms (0.2%)

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)

sample1.8s (79.5%)

Results

979.0ms	2783×	body	1024	valid
281.0ms	1365×	body	512	valid
251.0ms	3145×	body	128	valid
106.0ms	285×	body	2048	valid
99.0ms	678×	body	256	valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

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	40	6
6	59	6
7	100	6
8	146	6
9	222	6
10	349	6
11	507	6
12	579	6
13	615	6

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (0.2%)

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)

localize3.0ms (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)

rewrite38.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`log1p-expm1-u_binary64`
417×	`expm1-log1p-u_binary64`
286×	`unpow-prod-down_binary64`
219×	`log-prod_binary64`
117×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	83	6
2	1114	6

Stop Event

1×	node limit

Counts

1 → 70

Calls

1 calls:

37.0ms

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

simplify26.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

536×	`unswap-sqr_binary64`
502×	`associate-l_binary64`
484×	`fma-def_binary64`
309×	`associate-r_binary64`
186×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	91
1	68	89
2	145	86
3	393	79
4	981	76
5	3095	76

Stop Event

1×	node limit

Counts

82 → 80

prune39.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	2	81

Error

Counts

81 → 2

Alt Table

Status	Error	Program
▶	20.5b	(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 909 to 431 computations (52.6% saved)

localize7.0ms (0.3%)

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)
✓	0.1b	(fma.f64 x 1/24 1/6)

series6.0ms (0.3%)

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)

rewrite50.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log1p-expm1-u_binary64`
723×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
84×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	178	27
2	1882	27

Stop Event

1×	node limit

Counts

3 → 69

Calls

3 calls:

49.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
49.0ms	(fma.f64 x (fma.f64 x 1/24 1/6) 1/2)
49.0ms	(fma.f64 x 1/24 1/6)

simplify75.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

536×	`unswap-sqr_binary64`
522×	`associate-l_binary64`
482×	`distribute-rgt-in_binary64`
437×	`fma-def_binary64`
320×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	363
1	68	341
2	133	293
3	290	264
4	711	258
5	2244	258
6	3572	258
7	4096	258

Stop Event

1×	node limit

Counts

105 → 94

prune66.0ms (3%)

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
✓	20.5b	(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)

regimes35.0ms (1.6%)

Accuracy

Total 0.0b remaining (85.9%)

Threshold costs 0.0b (85.9%)

Counts

15 → 1

Compiler

Compiled 309 to 235 computations (23.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6

Stop Event

1×

saturated

end81.0ms (3.7%)

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	40	6
6	59	6
7	100	6
8	146	6
9	222	6
10	349	6
11	507	6
12	579	6
13	615	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	146	6
9	222	6
10	349	6
11	507	6
12	579	6
13	615	6

Details

analyze4.0ms (0.2%)

sample1.8s (79.5%)

simplify13.0ms (0.6%)

prune5.0ms (0.2%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite38.0ms (1.7%)

simplify26.0ms (1.2%)

prune39.0ms (1.8%)

localize7.0ms (0.3%)

series6.0ms (0.3%)

rewrite50.0ms (2.3%)

simplify75.0ms (3.4%)

prune66.0ms (3%)

regimes35.0ms (1.6%)

simplify2.0ms (0.1%)

end81.0ms (3.7%)

Profiling

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	146	6
9	222	6
10	349	6
11	507	6
12	579	6
13	615	6