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)

sample2.2s (65.7%)

Results

1.3s	2690×	body	1024	valid
291.0ms	1368×	body	512	valid
275.0ms	3169×	body	128	valid
114.0ms	754×	body	256	valid
105.0ms	275×	body	2048	valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify15.0ms (0.5%)

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)

localize4.0ms (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)

rewrite76.0ms (2.3%)

Algorithm

2×	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:

75.0ms

(/.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
0	0	0
1	0	0

simplify76.0ms (2.3%)

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

prune36.0ms (1.1%)

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
▶	1.8b	(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
✓	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 761 to 369 computations (51.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (expm1.f64 x) x)
✓	0.0b	(sqrt.f64 (/.f64 (expm1.f64 x) x))
✓	1.8b	(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
✓	3.9b	(log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)))

series535.0ms (16.2%)

Counts

3 → 12

Calls

3 calls:

237.0ms	(sqrt.f64 (/.f64 (expm1.f64 x) x))
234.0ms	(log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)))
64.0ms	(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))

rewrite115.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

696×	`log1p-expm1-u_binary64`
696×	`expm1-log1p-u_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`
127×	`log-pow_binary64`

Counts

3 → 111

Calls

3 calls:

113.0ms	(sqrt.f64 (/.f64 (expm1.f64 x) x))
113.0ms	(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
113.0ms	(log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	160	24
2	1846	24
3	4916	24
0	0	0
1	0	0

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
741×	`cancel-sign-sub-inv_binary64`
603×	`fma-neg_binary64`
501×	`associate-l_binary64`
468×	`unswap-sqr_binary64`

Counts

123 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	148
1	113	140
2	277	131
3	776	111
4	2409	111
5	5053	111

prune117.0ms (3.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	202	2	204

Error

Counts

204 → 2

Alt Table

Status	Error	Program
✓	1.8b	(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
✓	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 2616 to 1425 computations (45.5% saved)

regimes49.0ms (1.5%)

Accuracy

Total 0.0b remaining (33.8%)

Threshold costs 0.0b (33.8%)

Counts

19 → 1

Compiler

Compiled 329 to 251 computations (23.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end37.0ms (1.1%)

Compiler: Compiled 25 to 17 computations (32% 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%)

sample2.2s (65.7%)

simplify15.0ms (0.5%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite76.0ms (2.3%)

simplify76.0ms (2.3%)

prune36.0ms (1.1%)

localize7.0ms (0.2%)

series535.0ms (16.2%)

rewrite115.0ms (3.5%)

simplify51.0ms (1.5%)

prune117.0ms (3.5%)

regimes49.0ms (1.5%)

simplify2.0ms (0.1%)

end37.0ms (1.1%)

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