Details

analyze22.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample46.0ms (2.2%)

Algorithm

1×

intervals

Results

20.0ms	69×	body	1024	valid
9.0ms	128×	body	128	valid
7.0ms	42×	body	512	valid
2.0ms	5×	body	2048	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

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

30.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.7b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.3b	(-.f64 (log1p.f64 N) (log.f64 N))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
11×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`

Counts

1 → 39

Calls

1 calls:

4.0ms

(-.f64 (log1p.f64 N) (log.f64 N))

series11.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

11.0ms

(-.f64 (log1p.f64 N) (log.f64 N))

simplify119.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

435×	`fma-neg_binary64`
299×	`fma-def_binary64`
276×	`associate-l_binary64`
252×	`associate-/r*_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

51 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	928
1	214	635
2	600	575
3	2045	572
4	4184	572
5	4526	572
6	4942	572
7	4836	572

prune29.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	2	87

Error

0.0b

Counts

87 → 2

Alt Table

Status	Error	Program
	31.1b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
▶	30.6b	(log.f64 (/.f64 (+.f64 1 N) N))

Compiler

Compiled 864 to 293 computations (66.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 N) N)
✓	2.2b	(log.f64 (/.f64 (+.f64 1 N) N))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`

Counts

2 → 64

Calls

2 calls:

4.0ms	(/.f64 (+.f64 1 N) N)
3.0ms	(log.f64 (/.f64 (+.f64 1 N) N))

series13.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(/.f64 (+.f64 1 N) N)
4.0ms	(log.f64 (/.f64 (+.f64 1 N) N))

simplify92.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
443×	`distribute-rgt-in_binary64`
395×	`associate-/l/_binary64`
394×	`fma-neg_binary64`
377×	`distribute-lft-in_binary64`

Counts

88 → 154

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1207
1	263	1146
2	664	1124
3	1868	1117
4	4464	1079
5	4932	1079

prune56.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	152	4	156

Error

0.0b

Counts

156 → 4

Alt Table

Status	Error	Program
	0.5b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))
✓	30.6b	(log.f64 (/.f64 (+.f64 1 N) N))
▶	0.5b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
	3.7b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))

Compiler

Compiled 1514 to 1048 computations (30.8% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 N))
	0.2b	(sqrt.f64 (log1p.f64 (/.f64 1 N)))
✓	0.2b	(sqrt.f64 (log1p.f64 (/.f64 1 N)))
✓	0.5b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 79

Calls

3 calls:

5.0ms	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
1.0ms	(sqrt.f64 (log1p.f64 (/.f64 1 N)))
0.0ms	(log1p.f64 (/.f64 1 N))

series17.0ms (0.8%)

Counts

3 → 28

Calls

3 calls:

11.0ms	(sqrt.f64 (log1p.f64 (/.f64 1 N)))
3.0ms	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
3.0ms	(log1p.f64 (/.f64 1 N))

simplify130.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

639×	`cancel-sign-sub-inv_binary64`
588×	`fma-neg_binary64`
234×	`associate-/l/_binary64`
183×	`neg-mul-1_binary64`
168×	`associate-l_binary64`

Counts

107 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1403
1	239	1323
2	713	1267
3	2435	1210
4	4421	1210
5	4932	1210
6	4991	1210
7	4915	1210

prune82.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	211	3	214

Error

Counts

214 → 3

Alt Table

Status	Error	Program
	15.6b	(sqrt.f64 (pow.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) 4))
▶	0.0b	(log1p.f64 (/.f64 1 N))
	3.7b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))

Compiler

Compiled 2614 to 1969 computations (24.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (/.f64 1 N))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune12.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Error

Counts

38 → 3

Alt Table

Status	Error	Program
	15.6b	(sqrt.f64 (pow.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) 4))
✓	0.0b	(log1p.f64 (/.f64 1 N))
	3.7b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))

Compiler

Compiled 295 to 221 computations (25.1% saved)

regimes35.0ms (1.6%)

Accuracy

Total 0.0b remaining (14.7%)

Threshold costs 0.0b (14.7%)

Compiler

Compiled 406 to 288 computations (29.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
2	6	6

end0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample1.4s (65.3%)

Algorithm

1×

intervals

Results

536.0ms	1988×	body	1024	valid
290.0ms	4257×	body	128	valid
172.0ms	1012×	body	512	valid
99.0ms	247×	body	2048	valid
52.0ms	496×	body	256	valid

Compiler

Compiled 36 to 30 computations (16.7% saved)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Details

analyze22.0ms (1%)

sample46.0ms (2.2%)

simplify13.0ms (0.6%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

rewrite6.0ms (0.3%)

series11.0ms (0.5%)

simplify119.0ms (5.6%)

prune29.0ms (1.4%)

localize4.0ms (0.2%)

rewrite10.0ms (0.5%)

series13.0ms (0.6%)

simplify92.0ms (4.3%)

prune56.0ms (2.6%)

localize7.0ms (0.4%)

rewrite10.0ms (0.5%)

series17.0ms (0.8%)

simplify130.0ms (6.1%)

prune82.0ms (3.8%)

localize5.0ms (0.2%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.4%)

prune12.0ms (0.5%)

regimes35.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (65.3%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8