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)

sample1.7s (74.1%)

Results

865.0ms	2748×	body	1024	valid
321.0ms	1370×	body	512	valid
246.0ms	3131×	body	128	valid
105.0ms	290×	body	2048	valid
98.0ms	717×	body	256	valid

Compiler

Compiled 16 to 12 computations (25% saved)

preprocess37.0ms (1.7%)

Algorithm

2×	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
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 7 to 5 computations (28.6% 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

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

3 calls:

1.0ms	(/.f64 (expm1.f64 x) x)	x	-inf
1.0ms	(/.f64 (expm1.f64 x) x)	x	inf
1.0ms	(/.f64 (expm1.f64 x) x)	x	0

rewrite34.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

449×	`pow1_binary64`
417×	`add-log-exp_binary64`
417×	`log1p-expm1-u_binary64`
417×	`expm1-log1p-u_binary64`
407×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	83	6
2	1104	6

Stop Event

1×	node limit

Counts

1 → 32

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

44 → 42

prune24.0ms (1.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	2	43

Error

Counts

43 → 2

Alt Table

Status	Error	Program
	21.0b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)
▶	0.0b	(pow.f64 (/.f64 x (expm1.f64 x)) -1)

Compiler

Compiled 392 to 194 computations (50.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (expm1.f64 x))
✓	0.0b	(pow.f64 (/.f64 x (expm1.f64 x)) -1)

series25.0ms (1.1%)

Counts

2 → 24

Calls

6 calls:

9.0ms	(pow.f64 (/.f64 x (expm1.f64 x)) -1)	x	-inf
7.0ms	(pow.f64 (/.f64 x (expm1.f64 x)) -1)	x	inf
4.0ms	(/.f64 x (expm1.f64 x))	x	-inf
3.0ms	(/.f64 x (expm1.f64 x))	x	inf
1.0ms	(pow.f64 (/.f64 x (expm1.f64 x)) -1)	x	0

rewrite71.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

605×	`pow1_binary64`
565×	`add-log-exp_binary64`
565×	`log1p-expm1-u_binary64`
565×	`expm1-log1p-u_binary64`
61×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	125	12
2	1558	12

Stop Event

1×	node limit

Counts

2 → 74

simplify26.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
631×	`cancel-sign-sub-inv_binary64`
347×	`fma-def_binary64`
272×	`*-commutative_binary64`
238×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	186
1	93	180
2	218	173
3	657	158
4	2147	158

Stop Event

1×	node limit

Counts

98 → 90

prune52.0ms (2.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	90	2	92

Error

Counts

92 → 2

Alt Table

Status	Error	Program
▶	21.0b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)
✓	0.0b	(pow.f64 (/.f64 x (expm1.f64 x)) -1)

Compiler

Compiled 916 to 455 computations (50.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)
✓	0.1b	(fma.f64 x 1/6 1/2)

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 x (fma.f64 x 1/6 1/2) 1)	x	-inf
1.0ms	(fma.f64 x (fma.f64 x 1/6 1/2) 1)	x	inf
1.0ms	(fma.f64 x (fma.f64 x 1/6 1/2) 1)	x	0
1.0ms	(fma.f64 x 1/6 1/2)	x	-inf
0.0ms	(fma.f64 x 1/6 1/2)	x	inf

rewrite39.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`pow1_binary64`
540×	`add-log-exp_binary64`
540×	`log1p-expm1-u_binary64`
540×	`expm1-log1p-u_binary64`
531×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	136	14
2	1411	14

Stop Event

1×	node limit

Counts

2 → 42

simplify66.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

544×	`associate-l_binary64`
512×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
316×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	200
1	30	180
2	48	156
3	84	144
4	192	144
5	532	144
6	1786	144
7	3121	144
8	3327	144
9	3540	144
10	3760	144
11	4070	144
12	4472	144
13	4980	144

Stop Event

1×	node limit

Counts

66 → 55

prune28.0ms (1.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	55	2	57

Error

Counts

57 → 2

Alt Table

Status	Error	Program
✓	21.0b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)
✓	0.0b	(pow.f64 (/.f64 x (expm1.f64 x)) -1)

Compiler

Compiled 600 to 468 computations (22% saved)

regimes77.0ms (3.4%)

Accuracy

Total 0.0b remaining (51.9%)

Threshold costs 0.0b (51.9%)

Counts

20 → 1

Compiler

Compiled 333 to 237 computations (28.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	9	6

Stop Event

1×

saturated

end35.0ms (1.6%)

Stop Event

1×

done

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	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
0	1	1

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
0	1	1

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%)

sample1.7s (74.1%)

preprocess37.0ms (1.7%)

simplify13.0ms (0.6%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite34.0ms (1.5%)

simplify26.0ms (1.2%)

prune24.0ms (1.1%)

localize5.0ms (0.2%)

series25.0ms (1.1%)

rewrite71.0ms (3.2%)

simplify26.0ms (1.1%)

prune52.0ms (2.3%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite39.0ms (1.7%)

simplify66.0ms (2.9%)

prune28.0ms (1.3%)

regimes77.0ms (3.4%)

simplify2.0ms (0.1%)

end35.0ms (1.6%)

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
0	1	1

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