Details

analyze1.9s (21.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
3.1%	46.8%	50%	5
4.7%	45.3%	50%	6
5.5%	44.5%	50%	7
5.9%	44.1%	50%	8
6%	43.9%	50%	9
6.1%	43.8%	50%	10
6.2%	43.8%	50%	11
6.2%	43.7%	50%	12
6.2%	43.7%	50%	13
6.2%	43.7%	50%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample5.9s (69.3%)

Results

3.8s	4045×	body	1024	valid
1.1s	2123×	body	512	valid
545.0ms	443×	body	2048	valid
310.0ms	1030×	body	256	valid
93.0ms	615×	body	128	valid

Compiler

Compiled 34 to 26 computations (23.5% saved)

preprocess14.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
5×	`+-commutative_binary64`
4×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	14	10
2	19	10
3	25	10
4	33	10
5	43	10
6	57	10
7	73	10
8	77	10
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 8 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
5×	`+-commutative_binary64`
4×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	14	10
2	19	10
3	25	10
4	33	10
5	43	10
6	57	10
7	73	10
8	77	10

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.4b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
▶	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

Compiler

Compiled 50 to 38 computations (24% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

series14.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

6.0ms	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))	x	-inf
5.0ms	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))	x	inf
3.0ms	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))	x	0

rewrite32.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

402×	`expm1-log1p-u_binary64`
400×	`log1p-expm1-u_binary64`
313×	`unpow-prod-down_binary64`
216×	`log-prod_binary64`
113×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	124	8
2	1731	8

Stop Event

1×	node limit

Counts

1 → 70

simplify31.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

710×	`associate-/r*_binary64`
288×	`fma-def_binary64`
211×	`times-frac_binary64`
195×	`distribute-rgt-in_binary64`
150×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1007
1	409	993
2	1601	781

Stop Event

1×	node limit

Counts

82 → 93

prune49.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	92	3	95

Error

0.0b

Counts

95 → 3

Alt Table

Status	Error	Program
	61.4b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
▶	0.6b	(-.f64 -1 x)
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

Compiler

Compiled 2171 to 1307 computations (39.8% saved)

localize2.0ms (0%)

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	61.4b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
✓	0.6b	(-.f64 -1 x)
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

Compiler

Compiled 31 to 24 computations (22.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
✓	6.4b	(log.f64 (-.f64 1 x))
✓	6.4b	(log.f64 (+.f64 1 x))

series16.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

6.0ms	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))	x	-inf
5.0ms	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))	x	inf
1.0ms	(log.f64 (-.f64 1 x))	x	0
1.0ms	(log.f64 (+.f64 1 x))	x	0
1.0ms	(log.f64 (+.f64 1 x))	x	-inf

rewrite56.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`log1p-expm1-u_binary64`
815×	`expm1-log1p-u_binary64`
186×	`prod-diff_binary64`
81×	`add-sqr-sqrt_binary64`
76×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	169	18
2	2190	18

Stop Event

1×	node limit

Counts

3 → 75

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

517×	`fma-def_binary64`
288×	`times-frac_binary64`
265×	`distribute-rgt-in_binary64`
246×	`sub-neg_binary64`
231×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	1409
1	570	1361
2	2167	1153

Stop Event

1×	node limit

Counts

111 → 141

prune72.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	141	3	144

Error

Counts

144 → 3

Alt Table

Status	Error	Program
✓	61.4b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
✓	0.6b	(-.f64 -1 x)
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3))

Compiler

Compiled 2857 to 1931 computations (32.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3))
✓	0.0b	(pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3)

series54.0ms (0.6%)

Counts

2 → 24

Calls

6 calls:

24.0ms	(pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3)	x	inf
18.0ms	(pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3)	x	-inf
6.0ms	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3))	x	-inf
5.0ms	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3))	x	inf
1.0ms	(pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3)	x	0

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`expm1-log1p-u_binary64`
584×	`log1p-expm1-u_binary64`
113×	`prod-diff_binary64`
109×	`expm1-udef_binary64`
109×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	187	19
2	2297	19

Stop Event

1×	node limit

Counts

2 → 82

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

390×	`associate-+r+_binary64`
310×	`associate-/r*_binary64`
277×	`fma-def_binary64`
272×	`+-commutative_binary64`
247×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	2952
1	1055	2923
2	4792	2912

Stop Event

1×	node limit

Counts

106 → 127

prune156.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	220	3	223

Error

Counts

223 → 3

Alt Table

Status	Error	Program
✓	61.4b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
✓	0.6b	(-.f64 -1 x)
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 3))

Compiler

Compiled 7340 to 5036 computations (31.4% saved)

regimes25.0ms (0.3%)

Accuracy

Total 0.0b remaining (59.9%)

Threshold costs 0.0b (59.9%)

Counts

13 → 1

Compiler

Compiled 265 to 203 computations (23.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	10	10
2	12	10
3	13	10

Stop Event

1×

saturated

end49.0ms (0.6%)

Stop Event

1×

done

Compiler

Compiled 38 to 29 computations (23.7% saved)

Details

analyze1.9s (21.8%)

sample5.9s (69.3%)

preprocess14.0ms (0.2%)

simplify7.0ms (0.1%)

prune4.0ms (0%)

localize4.0ms (0%)

series14.0ms (0.2%)

rewrite32.0ms (0.4%)

simplify31.0ms (0.4%)

prune49.0ms (0.6%)

localize2.0ms (0%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series16.0ms (0.2%)

rewrite56.0ms (0.7%)

simplify43.0ms (0.5%)

prune72.0ms (0.8%)

localize6.0ms (0.1%)

series54.0ms (0.6%)

rewrite40.0ms (0.5%)

simplify71.0ms (0.8%)

prune156.0ms (1.8%)

regimes25.0ms (0.3%)

simplify2.0ms (0%)

end49.0ms (0.6%)

Profiling