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 (73.5%)

Results

994.0ms	2748×	body	1024	valid
302.0ms	1370×	body	512	valid
291.0ms	3131×	body	128	valid
110.0ms	717×	body	256	valid
110.0ms	290×	body	2048	valid

Compiler

Compiled 16 to 12 computations (25% saved)

preprocess25.0ms (1%)

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)

simplify17.0ms (0.7%)

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)

localize4.0ms (0.2%)

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 (1.4%)

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

simplify25.0ms (1%)

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

prune44.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	2	81

Error

Counts

81 → 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 912 to 434 computations (52.4% saved)

localize4.0ms (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)

series24.0ms (1%)

Counts

2 → 24

Calls

6 calls:

7.0ms	(pow.f64 (/.f64 x (expm1.f64 x)) -1)	x	inf
7.0ms	(pow.f64 (/.f64 x (expm1.f64 x)) -1)	x	-inf
5.0ms	(/.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

rewrite37.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

565×	`log1p-expm1-u_binary64`
565×	`expm1-log1p-u_binary64`
285×	`log-prod_binary64`
153×	`pow2_binary64`
106×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	125	12
2	1578	12

Stop Event

1×	node limit

Counts

2 → 83

simplify28.0ms (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

107 → 99

prune72.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	99	2	101

Error

Counts

101 → 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 1021 to 497 computations (51.3% 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
1.0ms	(fma.f64 x 1/6 1/2)	x	-inf

rewrite58.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

540×	`log1p-expm1-u_binary64`
540×	`expm1-log1p-u_binary64`
263×	`unpow-prod-down_binary64`
236×	`log-prod_binary64`
160×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	136	14
2	1419	14

Stop Event

1×	node limit

Counts

2 → 66

simplify77.0ms (3.1%)

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

90 → 79

prune47.0ms (1.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

81 → 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 1013 to 812 computations (19.8% saved)

regimes39.0ms (1.6%)

Accuracy

Total 0.0b remaining (51.9%)

Threshold costs 0.0b (51.9%)

Counts

21 → 1

Compiler

Compiled 345 to 247 computations (28.4% saved)

simplify4.0ms (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

end97.0ms (3.9%)

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%)

sample1.8s (73.5%)

preprocess25.0ms (1%)

simplify17.0ms (0.7%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite34.0ms (1.4%)

simplify25.0ms (1%)

prune44.0ms (1.8%)

localize4.0ms (0.2%)

series24.0ms (1%)

rewrite37.0ms (1.5%)

simplify28.0ms (1.1%)

prune72.0ms (2.9%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite58.0ms (2.4%)

simplify77.0ms (3.1%)

prune47.0ms (1.9%)

regimes39.0ms (1.6%)

simplify4.0ms (0.1%)

end97.0ms (3.9%)

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