Details

analyze713.0ms (13.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample177.0ms (3.3%)

Algorithm

1×

intervals

Results

13.0ms	193×	body	128	valid
9.0ms	30×	body	1024	valid
8.0ms	41×	body	1024	nan
3.0ms	17×	body	512	valid
2.0ms	17×	body	512	nan
2.0ms	5×	body	2048	valid
2.0ms	17×	body	256	nan
1.0ms	11×	body	256	valid
1.0ms	13×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify203.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

2748×	`fma-def_binary64`
1264×	`fma-neg_binary64`
934×	`associate--r-_binary64`
475×	`cancel-sign-sub-inv_binary64`
423×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	17
2	40	17
3	86	15
4	163	15
5	344	15
6	666	15
7	1217	15
8	1463	15
9	1608	15
10	1787	15
11	2322	15
12	2926	15
13	2987	15
14	3089	15
15	3133	15
16	3142	15
17	3142	15
18	3225	15
19	3233	15
20	3237	15
21	4979	15

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

15.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.7b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 y -1))
✓	1.3b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series64.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

55.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
8.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out--_binary64`

Counts

2 → 65

Calls

2 calls:

6.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))
0.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

479×	`associate-+r+_binary64`
403×	`sub-neg_binary64`
349×	`+-commutative_binary64`
306×	`associate-+l+_binary64`
240×	`associate-/r*_binary64`

Counts

113 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	377	3806
1	1121	3687
2	4545	3655
3	5244	3655

prune134.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	164	3	167

Error

0.1b

Counts

167 → 3

Alt Table

Status	Error	Program
✓	15.7b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
▶	46.8b	(-.f64 1 (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x))))))
	58.1b	(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))

Compiler

Compiled 5330 to 3509 computations (34.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x)))))
✓	0.1b	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
✓	0.2b	(/.f64 1 (*.f64 y (-.f64 1 x)))
✓	5.5b	(/.f64 x (*.f64 y (-.f64 1 x)))

series372.0ms (6.9%)

Counts

4 → 96

Calls

4 calls:

288.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
63.0ms	(+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x)))))
10.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))
10.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))

rewrite72.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`associate-+r+_binary64`
85×	`*-un-lft-identity_binary64`
81×	`prod-diff_binary64`
72×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`

Counts

4 → 224

Calls

4 calls:

25.0ms	(+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x)))))
6.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))
5.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))
4.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))

simplify238.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

315×	`associate-+l+_binary64`
214×	`distribute-rgt-in_binary64`
213×	`fma-neg_binary64`
194×	`distribute-lft-in_binary64`
191×	`associate-l_binary64`

Counts

320 → 369

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	475	10143
1	1274	8868
2	4539	8858
3	4926	8858
4	4972	8858

prune317.0ms (5.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	368	1	369
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	370	2	372

Error

Counts

372 → 2

Alt Table

Status	Error	Program
▶	41.4b	(-.f64 1 (log.f64 (*.f64 (/.f64 (neg.f64 (-.f64 1 x)) y) (exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y)))))
✓	15.7b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 17023 to 11134 computations (34.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 1 x))
✓	0.0b	(/.f64 (neg.f64 (-.f64 1 x)) y)
✓	0.0b	(exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y))
✓	4.0b	(*.f64 (/.f64 (neg.f64 (-.f64 1 x)) y) (exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y)))

series80.0ms (1.5%)

Counts

4 → 80

Calls

4 calls:

51.0ms	(*.f64 (/.f64 (neg.f64 (-.f64 1 x)) y) (exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y)))
20.0ms	(exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y))
6.0ms	(/.f64 (neg.f64 (-.f64 1 x)) y)
2.0ms	(/.f64 1 (-.f64 1 x))

rewrite132.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

277×	`*-un-lft-identity_binary64`
265×	`times-frac_binary64`
234×	`add-sqr-sqrt_binary64`
106×	`add-cube-cbrt_binary64`
79×	`exp-prod_binary64`

Counts

4 → 298

Calls

4 calls:

52.0ms	(*.f64 (/.f64 (neg.f64 (-.f64 1 x)) y) (exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y)))
32.0ms	(exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y))
7.0ms	(/.f64 (neg.f64 (-.f64 1 x)) y)
4.0ms	(/.f64 1 (-.f64 1 x))

simplify256.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
209×	`sub-neg_binary64`
193×	`div-sub_binary64`
192×	`associate-/r*_binary64`
171×	`associate-/l*_binary64`

Counts

378 → 434

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	445	8761
1	1044	8224
2	3427	8168
3	4836	8168
4	4991	8168
5	4954	8168

prune323.0ms (6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	434	0	434
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	434	2	436

Error

Counts

436 → 2

Alt Table

Status	Error	Program
✓	41.4b	(-.f64 1 (log.f64 (*.f64 (/.f64 (neg.f64 (-.f64 1 x)) y) (exp.f64 (/.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (/.f64 x (-.f64 1 x))) y)))))
✓	15.7b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 15487 to 11200 computations (27.7% saved)

regimes625.0ms (11.6%)

Accuracy

Total 0.4b remaining (93.8%)

Threshold costs 0.4b (93.8%)

Counts

68 → 2

Compiler

Compiled 8126 to 6256 computations (23% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	65
1	43	65
2	60	65
3	70	65
4	75	65
5	74	65

end1.0ms (0%)

Compiler: Compiled 45 to 32 computations (28.9% saved)

sample1.6s (28.8%)

Algorithm

1×

intervals

Results

387.0ms	5820×	body	128	valid
264.0ms	1049×	body	1024	valid
203.0ms	997×	body	1024	nan
119.0ms	663×	body	512	valid
93.0ms	638×	body	512	nan
44.0ms	397×	body	256	valid
36.0ms	360×	body	256	nan
24.0ms	71×	body	2048	valid
19.0ms	420×	body	128	nan
0.0ms	2×	body	2048	nan

Compiler

Compiled 100 to 75 computations (25% saved)

Details

analyze713.0ms (13.2%)

sample177.0ms (3.3%)

simplify203.0ms (3.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series64.0ms (1.2%)

rewrite11.0ms (0.2%)

simplify93.0ms (1.7%)

prune134.0ms (2.5%)

localize14.0ms (0.3%)

series372.0ms (6.9%)

rewrite72.0ms (1.3%)

simplify238.0ms (4.4%)

prune317.0ms (5.8%)

localize13.0ms (0.2%)

series80.0ms (1.5%)

rewrite132.0ms (2.4%)

simplify256.0ms (4.7%)

prune323.0ms (6%)

regimes625.0ms (11.6%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (28.8%)

Profiling