Details

analyze39.0ms (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)

sample86.0ms (2.3%)

Algorithm

1×

intervals

Results

32.0ms	56×	body	1024	valid
17.0ms	143×	body	128	valid
12.0ms	9×	body	2048	valid
9.0ms	26×	body	512	valid
4.0ms	22×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify23.0ms (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

prune5.0ms (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

27.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.6b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 N)
✓	2.5b	(-.f64 (log1p.f64 N) (log.f64 N))

series11.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(-.f64 (log1p.f64 N) (log.f64 N))
5.0ms	(log1p.f64 N)

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
12×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`

Counts

2 → 50

Calls

2 calls:

9.0ms	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	(log1p.f64 N)

simplify160.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-neg_binary64`
443×	`fma-def_binary64`
358×	`sub-neg_binary64`
331×	`associate-l_binary64`
273×	`associate-r_binary64`

Counts

74 → 89

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	128	1171
1	285	854
2	840	790
3	2888	783
4	4203	783
5	4702	779
6	4961	779
7	4814	779

prune81.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Error

0.0b

Counts

90 → 4

Alt Table

Status	Error	Program
▶	27.6b	(-.f64 (-.f64 (log1p.f64 N) (log.f64 (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
	28.0b	(log.f64 (/.f64 (+.f64 1 N) N))
✓	27.6b	(-.f64 (log1p.f64 N) (log.f64 N))
	33.2b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

Compiler

Compiled 1305 to 540 computations (58.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 N)
✓	0.0b	(log.f64 (sqrt.f64 N))
✓	0.0b	(-.f64 (log1p.f64 N) (log.f64 (sqrt.f64 N)))
✓	2.4b	(-.f64 (-.f64 (log1p.f64 N) (log.f64 (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))

series67.0ms (1.8%)

Counts

3 → 0

Calls

3 calls:

27.0ms	(-.f64 (log1p.f64 N) (log.f64 (sqrt.f64 N)))
24.0ms	(-.f64 (-.f64 (log1p.f64 N) (log.f64 (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
16.0ms	(log.f64 (sqrt.f64 N))

rewrite70.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
72×	`prod-diff_binary64`
62×	`add-sqr-sqrt_binary64`
61×	`log-pow_binary64`
48×	`pow1_binary64`

Counts

3 → 171

Calls

3 calls:

25.0ms	(-.f64 (-.f64 (log1p.f64 N) (log.f64 (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
10.0ms	(-.f64 (log1p.f64 N) (log.f64 (sqrt.f64 N)))
3.0ms	(log.f64 (sqrt.f64 N))

simplify381.0ms (10%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-def_binary64`
376×	`associate-l_binary64`
375×	`fma-neg_binary64`
317×	`associate-r_binary64`
290×	`log-prod_binary64`

Counts

171 → 197

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	156	4289
1	269	2484
2	817	2027
3	3192	2025
4	4105	2019
5	4798	1604
6	4813	1604
7	4976	1604
8	4987	1604
9	4928	1604

prune214.0ms (5.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	252	2	254
Fresh	0	2	2
Picked	1	0	1
Done	1	0	1
Total	254	4	258

Error

0.0b

Counts

258 → 4

Alt Table

Status	Error	Program
	28.0b	(log.f64 (/.f64 (+.f64 1 N) N))
	27.6b	(-.f64 (+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N)))) (log.f64 (sqrt.f64 N)))
▶	27.5b	(-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
	33.2b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

Compiler

Compiled 5350 to 1415 computations (73.6% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N)))
	0.0b	(log.f64 (sqrt.f64 N))
✓	0.4b	(/.f64 (+.f64 1 N) (sqrt.f64 N))
✓	2.7b	(-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))

series87.0ms (2.3%)

Counts

3 → 8

Calls

3 calls:

40.0ms	(-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
27.0ms	(log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N)))
20.0ms	(/.f64 (+.f64 1 N) (sqrt.f64 N))

rewrite72.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
72×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`
62×	`log-prod_binary64`

Counts

3 → 178

Calls

3 calls:

22.0ms	(-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
15.0ms	(/.f64 (+.f64 1 N) (sqrt.f64 N))
7.0ms	(log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N)))

simplify200.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

999×	`fma-neg_binary64`
737×	`fma-def_binary64`
237×	`cancel-sign-sub-inv_binary64`
209×	`distribute-rgt-in_binary64`
183×	`sub-neg_binary64`

Counts

186 → 237

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	224	3901
1	454	3388
2	1309	3089
3	3846	2812
4	4680	2810
5	4993	2810

prune149.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	260	5	265

Error

0.0b

Counts

265 → 5

Alt Table

Status	Error	Program
	28.0b	(log.f64 (/.f64 (+.f64 1 N) N))
▶	27.6b	(-.f64 (+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N)))) (log.f64 (sqrt.f64 N)))
	28.1b	(exp.f64 (log.f64 (-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))))
✓	27.5b	(-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
	33.2b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

Compiler

Compiled 5298 to 2643 computations (50.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 N)
	0.0b	(log.f64 (sqrt.f64 N))
✓	0.0b	(+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N))))
✓	2.4b	(-.f64 (+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N)))) (log.f64 (sqrt.f64 N)))

series25.0ms (0.7%)

Counts

2 → 0

Calls

2 calls:

13.0ms	(-.f64 (+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N)))) (log.f64 (sqrt.f64 N)))
11.0ms	(+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N))))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
36×	`prod-diff_binary64`
35×	`log-pow_binary64`
30×	`distribute-lft-out_binary64`
30×	`pow1_binary64`

Counts

2 → 113

Calls

2 calls:

12.0ms	(-.f64 (+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N)))) (log.f64 (sqrt.f64 N)))
6.0ms	(+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N))))

simplify185.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

668×	`unsub-neg_binary64`
459×	`fma-neg_binary64`
405×	`distribute-rgt-in_binary64`
337×	`distribute-lft-in_binary64`
292×	`sub-neg_binary64`

Counts

113 → 114

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	131	3622
1	286	1950
2	1119	1659
3	3099	1594
4	3895	1594
5	4473	1594
6	4942	1141
7	4771	1141

prune98.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	195	5	200

Error

0.0b

Counts

200 → 5

Alt Table

Status	Error	Program
	28.0b	(log.f64 (/.f64 (+.f64 1 N) N))
✓	27.6b	(-.f64 (+.f64 (log1p.f64 N) (neg.f64 (log.f64 (sqrt.f64 N)))) (log.f64 (sqrt.f64 N)))
	28.1b	(exp.f64 (log.f64 (-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))))
✓	27.5b	(-.f64 (log.f64 (/.f64 (+.f64 1 N) (sqrt.f64 N))) (log.f64 (sqrt.f64 N)))
	33.2b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

Compiler

Compiled 3691 to 966 computations (73.8% saved)

regimes88.0ms (2.3%)

Accuracy

Total 0.0b remaining (28.1%)

Threshold costs 0.0b (28.1%)

Counts

40 → 2

Compiler

Compiled 980 to 612 computations (37.6% saved)

bsearch15.0ms (0.4%)

Steps

Iters	Range		Point
8	790.2198404473061	395905.25614255416	6013.484448010823

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	31	46
2	41	46
3	45	46
4	47	46
5	45	46

end1.0ms (0%)

Compiler: Compiled 31 to 22 computations (29% saved)

sample1.7s (43.5%)

Algorithm

1×

intervals

Results

601.0ms	2042×	body	1024	valid
324.0ms	4223×	body	128	valid
260.0ms	1006×	body	512	valid
105.0ms	231×	body	2048	valid
62.0ms	498×	body	256	valid

Compiler

Compiled 102 to 72 computations (29.4% 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

analyze39.0ms (1%)

sample86.0ms (2.3%)

simplify23.0ms (0.6%)

prune5.0ms (0.1%)

localize11.0ms (0.3%)

series11.0ms (0.3%)

rewrite15.0ms (0.4%)

simplify160.0ms (4.2%)

prune81.0ms (2.1%)

localize13.0ms (0.3%)

series67.0ms (1.8%)

rewrite70.0ms (1.8%)

simplify381.0ms (10%)

prune214.0ms (5.6%)

localize18.0ms (0.5%)

series87.0ms (2.3%)

rewrite72.0ms (1.9%)

simplify200.0ms (5.3%)

prune149.0ms (3.9%)

localize7.0ms (0.2%)

series25.0ms (0.7%)

rewrite28.0ms (0.7%)

simplify185.0ms (4.9%)

prune98.0ms (2.6%)

regimes88.0ms (2.3%)

bsearch15.0ms (0.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (43.5%)

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