Details

analyze828.0ms (5.1%)

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
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	50%	0.1%	7
50%	50%	0.1%	8
50%	50%	0.1%	9
50%	50%	0.1%	10
50%	50%	0.1%	11
50%	50%	0.1%	12
50%	50%	0.1%	13
50%	50%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample13.0s (79.5%)

Symmetry

(sort a b)

Results

10.0s	7838×	body	8192	exit
1.4s	1972×	body	1024	valid
716.0ms	4565×	body	128	valid
449.0ms	1032×	body	512	valid
208.0ms	216×	body	2048	valid
126.0ms	471×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	3.0b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series458.0ms (2.8%)

Counts

2 → 48

Calls

2 calls:

453.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
3.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
418×	`associate-+l+_binary64`
392×	`fma-def_binary64`
238×	`times-frac_binary64`
229×	`associate-+r+_binary64`

Counts

82 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1238
1	334	1183
2	1034	1155
3	4062	1151
4	4828	1151
5	4973	1151

prune58.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Error

0.4b

Counts

84 → 2

Alt Table

Status	Error	Program
▶	0.9b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	34.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1345 to 608 computations (54.8% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 a))
✓	0.0b	(+.f64 1 (exp.f64 a))

series194.0ms (1.2%)

Counts

2 → 16

Calls

2 calls:

193.0ms	(log1p.f64 (exp.f64 a))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

4.0ms	(+.f64 1 (exp.f64 a))
0.0ms	(log1p.f64 (exp.f64 a))

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

917×	`fma-neg_binary64`
564×	`fma-def_binary64`
478×	`associate-+l+_binary64`
423×	`cancel-sign-sub-inv_binary64`
417×	`distribute-rgt-neg-in_binary64`

Counts

44 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	351
1	148	322
2	306	320
3	749	307
4	2078	307
5	3781	307
6	4950	307
7	4994	307
8	4897	307

prune32.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Error

0.4b

Counts

47 → 3

Alt Table

Status	Error	Program
▶	0.9b	(+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))
	0.9b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
	34.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 742 to 414 computations (44.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (exp.f64 a))
✓	0.0b	(exp.f64 (log.f64 (log1p.f64 (exp.f64 a))))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.3b	(log.f64 (log1p.f64 (exp.f64 a)))

series631.0ms (3.9%)

Counts

2 → 24

Calls

2 calls:

404.0ms	(log.f64 (log1p.f64 (exp.f64 a)))
227.0ms	(exp.f64 (log.f64 (log1p.f64 (exp.f64 a))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

1.0ms	(exp.f64 (log.f64 (log1p.f64 (exp.f64 a))))
1.0ms	(log.f64 (log1p.f64 (exp.f64 a)))

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

662×	`associate-/l*_binary64`
662×	`fma-neg_binary64`
520×	`cancel-sign-sub-inv_binary64`
386×	`associate-/r*_binary64`
201×	`associate-/l/_binary64`

Counts

55 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	612
1	163	569
2	420	550
3	1560	536
4	4475	536
5	5008	536

prune66.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	100	3	103

Error

0.4b

Counts

103 → 3

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))
▶	0.9b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
	34.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1835 to 969 computations (47.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (exp.f64 a))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
✓	0.4b	(log1p.f64 (+.f64 1 (exp.f64 a)))

series194.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

192.0ms	(log1p.f64 (+.f64 1 (exp.f64 a)))
2.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (+.f64 1 (exp.f64 a)))
0.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1017×	`fma-def_binary64`
626×	`associate-*l/_binary64`
298×	`*-commutative_binary64`
275×	`distribute-rgt-out_binary64`
273×	`distribute-rgt-in_binary64`

Counts

46 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	411
1	99	378
2	228	378
3	525	367
4	1112	364
5	2190	364
6	2879	364
7	3136	364
8	5311	364

prune67.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	97	3	100

Error

0.4b

Counts

100 → 3

Alt Table

Status	Error	Program
	2.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))))
✓	0.9b	(+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))
	34.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1611 to 948 computations (41.2% saved)

regimes256.0ms (1.6%)

Accuracy

Total 0.6b remaining (60.9%)

Threshold costs 0.6b (60.9%)

Counts

54 → 1

Compiler

Compiled 4099 to 3168 computations (22.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	15	20
2	14	20

end208.0ms (1.3%)

Compiler: Compiled 111 to 79 computations (28.8% saved)

Details

analyze828.0ms (5.1%)

sample13.0s (79.5%)

simplify6.0ms (0%)

prune3.0ms (0%)

localize5.0ms (0%)

series458.0ms (2.8%)

rewrite9.0ms (0.1%)

simplify86.0ms (0.5%)

prune58.0ms (0.4%)

localize6.0ms (0%)

series194.0ms (1.2%)

rewrite5.0ms (0%)

simplify87.0ms (0.5%)

prune32.0ms (0.2%)

localize11.0ms (0.1%)

series631.0ms (3.9%)

rewrite3.0ms (0%)

simplify59.0ms (0.4%)

prune66.0ms (0.4%)

localize13.0ms (0.1%)

series194.0ms (1.2%)

rewrite1.0ms (0%)

simplify64.0ms (0.4%)

prune67.0ms (0.4%)

regimes256.0ms (1.6%)

simplify2.0ms (0%)

end208.0ms (1.3%)

Profiling