Details

analyze765.0ms (12.9%)

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
0%	99.9%	0.1%	5
3.1%	93.7%	3.2%	6
15.6%	73.4%	11%	7
20.3%	67.9%	11.8%	8
28.9%	55.8%	15.3%	9
31.6%	52.9%	15.5%	10
36.1%	46.7%	17.2%	11
37.6%	45.2%	17.2%	12
39.9%	42.1%	18%	13
40.6%	41.3%	18%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample2.2s (37.4%)

Results

793.0ms	5999×	body	128	valid
453.0ms	1069×	body	1024	valid
260.0ms	1594×	body	128	invalid
222.0ms	728×	body	512	valid
197.0ms	509×	body	1024	invalid
100.0ms	336×	body	512	invalid
85.0ms	382×	body	256	valid
44.0ms	184×	body	256	invalid
41.0ms	78×	body	2048	valid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess30.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

668×	`fma-neg_binary64`
504×	`times-frac_binary64`
448×	`div-sub_binary64`
360×	`fma-def_binary64`
276×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	38	34
2	73	30
3	160	30
4	352	30
5	807	30
6	2207	30
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1074×	`fma-def_binary64`
781×	`fma-neg_binary64`
314×	`div-sub_binary64`
282×	`times-frac_binary64`
194×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	17
2	40	17
3	86	15
4	196	15
5	431	15
6	1016	15
7	2510	15
8	4117	15
9	4867	15

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

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

20.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.4b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 y -1))
✓	2.4b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series86.0ms (1.5%)

Counts

3 → 72

Calls

18 calls:

16.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))	x	inf
16.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))	x	-inf
13.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))	x	inf
12.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))	x	-inf
5.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))	y	-inf

rewrite62.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

338×	`fma-def_binary64`
204×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
174×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	225	37
2	3223	37

Stop Event

1×	node limit

Counts

3 → 113

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

661×	`associate-+r+_binary64`
407×	`associate-+l+_binary64`
237×	`associate--r+_binary64`
225×	`associate-/r*_binary64`
193×	`associate--l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	366	4967
1	1282	4869

Stop Event

1×	node limit

Counts

185 → 229

prune197.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	227	3	230

Error

0.1b

Counts

230 → 3

Alt Table

Status	Error	Program
	55.1b	(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))
▶	45.3b	(-.f64 1 (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y))))
✓	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 8767 to 6090 computations (30.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y))
✓	0.0b	(+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y)))
✓	0.1b	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
✓	1.0b	(/.f64 1 (*.f64 y (-.f64 1 x)))

series279.0ms (4.7%)

Counts

4 → 96

Calls

24 calls:

65.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))	y	0
60.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))	y	inf
59.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))	y	-inf
16.0ms	(+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y)))	y	inf
16.0ms	(+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y)))	y	-inf

rewrite55.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

194×	`add-sqr-sqrt_binary64`
186×	`add-cbrt-cube_binary64`
186×	`expm1-log1p-u_binary64`
185×	`log1p-expm1-u_binary64`
180×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	82
1	395	60

Stop Event

1×	node limit

Counts

4 → 147

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

412×	`associate--r+_binary64`
329×	`associate-+l+_binary64`
319×	`associate--l+_binary64`
309×	`fma-neg_binary64`
297×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	124	1892
1	362	1764
2	1161	1764
3	4825	1764

Stop Event

1×	node limit

Counts

243 → 217

prune162.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	217	3	220

Error

0.1b

Counts

220 → 3

Alt Table

Status	Error	Program
▶	55.1b	(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))
✓	45.3b	(-.f64 1 (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y))))
✓	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 7841 to 5476 computations (30.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (log.f64 (+.f64 x -1)) (log.f64 y))

series182.0ms (3.1%)

Counts

1 → 24

Calls

6 calls:

61.0ms	(-.f64 (log.f64 (+.f64 x -1)) (log.f64 y))	y	inf
60.0ms	(-.f64 (log.f64 (+.f64 x -1)) (log.f64 y))	y	-inf
58.0ms	(-.f64 (log.f64 (+.f64 x -1)) (log.f64 y))	y	0
1.0ms	(-.f64 (log.f64 (+.f64 x -1)) (log.f64 y))	x	-inf
1.0ms	(-.f64 (log.f64 (+.f64 x -1)) (log.f64 y))	x	inf

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

883×	`log1p-expm1-u_binary64`
883×	`expm1-log1p-u_binary64`
431×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	171	9
2	2267	9

Stop Event

1×	node limit

Counts

1 → 49

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-def_binary64`
416×	`distribute-neg-in_binary64`
389×	`sub-neg_binary64`
368×	`distribute-rgt-in_binary64`
277×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	378
1	190	348
2	624	340
3	2564	337

Stop Event

1×	node limit

Counts

73 → 73

prune38.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	73	3	76

Error

Counts

76 → 3

Alt Table

Status	Error	Program
✓	45.3b	(-.f64 1 (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y))))
✓	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
▶	36.5b	(-.f64 1 (log.f64 (/.f64 (+.f64 x -1) y)))

Compiler

Compiled 1336 to 914 computations (31.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log.f64 (/.f64 (+.f64 x -1) y)))
✓	0.0b	(/.f64 (+.f64 x -1) y)
✓	3.1b	(log.f64 (/.f64 (+.f64 x -1) y))

series346.0ms (5.8%)

Counts

3 → 72

Calls

18 calls:

62.0ms	(log.f64 (/.f64 (+.f64 x -1) y))	y	0
56.0ms	(-.f64 1 (log.f64 (/.f64 (+.f64 x -1) y)))	y	inf
55.0ms	(log.f64 (/.f64 (+.f64 x -1) y))	y	-inf
54.0ms	(-.f64 1 (log.f64 (/.f64 (+.f64 x -1) y)))	y	0
53.0ms	(log.f64 (/.f64 (+.f64 x -1) y))	y	inf

rewrite56.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

430×	`log-prod_binary64`
223×	`prod-diff_binary64`
169×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`
163×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	192	28
2	2502	28

Stop Event

1×	node limit

Counts

3 → 154

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

782×	`sub-neg_binary64`
532×	`fma-neg_binary64`
370×	`associate-+l+_binary64`
298×	`associate--l+_binary64`
245×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	1019
1	259	983
2	871	975
3	3943	975

Stop Event

1×	node limit

Counts

226 → 214

prune108.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	214	3	217

Error

Counts

217 → 3

Alt Table

Status	Error	Program
✓	45.3b	(-.f64 1 (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (/.f64 (/.f64 x (-.f64 1 x)) y))))
✓	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	36.5b	(-.f64 1 (log.f64 (/.f64 (+.f64 x -1) y)))

Compiler

Compiled 3419 to 2540 computations (25.7% saved)

regimes733.0ms (12.4%)

Accuracy

Total 0.1b remaining (80.4%)

Threshold costs 0.1b (80.4%)

Counts

79 → 3

Compiler

Compiled 8804 to 6898 computations (21.6% saved)

bsearch209.0ms (3.5%)

Algorithm

2×	binary-search

Calls

2 calls:

182.0ms	y
24.0ms	y

Steps

Iters	Point		Range
5977358701217.452	∈ [	0.0023587930517268364	,	4.969167360682864e+38	]
-546459.0231533627	∈ [	-23862051.640595168	,	-0.00260639389025891	]

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
13×	`sub-neg_binary64`
10×	`*-commutative_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	74
1	51	74
2	69	74
3	88	74
4	102	74
5	108	74
6	110	74

Stop Event

1×

saturated

end71.0ms (1.2%)

Stop Event

1×

done

Compiler

Compiled 150 to 114 computations (24% saved)

Details

analyze765.0ms (12.9%)

sample2.2s (37.4%)

preprocess30.0ms (0.5%)

simplify35.0ms (0.6%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series86.0ms (1.5%)

rewrite62.0ms (1%)

simplify67.0ms (1.1%)

prune197.0ms (3.3%)

localize15.0ms (0.3%)

series279.0ms (4.7%)

rewrite55.0ms (0.9%)

simplify63.0ms (1.1%)

prune162.0ms (2.7%)

localize6.0ms (0.1%)

series182.0ms (3.1%)

rewrite43.0ms (0.7%)

simplify28.0ms (0.5%)

prune38.0ms (0.6%)

localize6.0ms (0.1%)

series346.0ms (5.8%)

rewrite56.0ms (0.9%)

simplify48.0ms (0.8%)

prune108.0ms (1.8%)

regimes733.0ms (12.4%)

bsearch209.0ms (3.5%)

simplify4.0ms (0.1%)

end71.0ms (1.2%)

Profiling