Details

analyze779.0ms (3.8%)

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)

sample13.1s (64.6%)

Symmetry

(sort a b)

Results

10.3s	7975×	body	8192	exit
1.4s	1995×	body	1024	valid
649.0ms	4582×	body	128	valid
437.0ms	1028×	body	512	valid
186.0ms	207×	body	2048	valid
114.0ms	444×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify5.0ms (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

prune2.0ms (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

30.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.2b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series437.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

432.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite164.0ms (0.8%)

Algorithm

2×	egg-rewrite

Rules

40×	`egg`
22×	`egg`

Counts

2 → 62

Calls

2 calls:

111.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
51.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	137	10
2	1701	10
3	4952	10
0	6	8
1	121	8
2	1530	8
3	4841	8
4	4780	8
5	4971	8

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-neg_binary64`
407×	`associate-+l+_binary64`
328×	`fma-def_binary64`
238×	`times-frac_binary64`
222×	`associate-+r+_binary64`

Counts

110 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	746
1	244	742
2	857	714
3	3662	710
4	4952	710
5	4990	710

prune58.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Error

1.2b

Counts

93 → 3

Alt Table

Status	Error	Program
	30.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	30.2b	(log1p.f64 (-.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 1))
▶	2.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1443 to 730 computations (49.4% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

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

series265.0ms (1.3%)

Counts

3 → 32

Calls

3 calls:

245.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
18.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite265.0ms (1.3%)

Algorithm

3×	egg-rewrite

Rules

56×	`egg`
51×	`egg`
45×	`egg`

Counts

3 → 152

Calls

3 calls:

98.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
83.0ms	(+.f64 1 (exp.f64 a))
81.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	98	6
2	1121	6
3	4710	6
4	5154	6
0	9	16
1	187	16
2	2486	16
3	4739	16
4	5016	16
0	7	9
1	143	9
2	1798	9
3	4988	9
4	4978	9

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-+l+_binary64`
473×	`distribute-rgt-neg-in_binary64`
412×	`distribute-lft-neg-in_binary64`
362×	`associate-l_binary64`
357×	`cancel-sign-sub-inv_binary64`

Counts

184 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	501
1	148	482
2	421	466
3	1291	462
4	3209	462
5	4511	462
6	4977	462
7	4945	462

prune136.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	174	6	180

Error

1.2b

Counts

180 → 6

Alt Table

Status	Error	Program
	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))))
	28.4b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b 2))
	30.2b	(log1p.f64 (-.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 1))
▶	2.2b	(fma.f64 (/.f64 1 (+.f64 (exp.f64 a) 1)) b (log1p.f64 (exp.f64 a)))
	2.9b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2) (log1p.f64 (exp.f64 a)))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))

Compiler

Compiled 3099 to 1672 computations (46% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

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

series358.0ms (1.8%)

Counts

3 → 48

Calls

3 calls:

347.0ms	(fma.f64 (/.f64 1 (+.f64 (exp.f64 a) 1)) b (log1p.f64 (exp.f64 a)))
8.0ms	(/.f64 1 (+.f64 (exp.f64 a) 1))
2.0ms	(+.f64 (exp.f64 a) 1)

rewrite317.0ms (1.6%)

Algorithm

3×	egg-rewrite

Rules

53×	`egg`
45×	`egg`
25×	`egg`

Counts

3 → 123

Calls

3 calls:

173.0ms	(fma.f64 (/.f64 1 (+.f64 (exp.f64 a) 1)) b (log1p.f64 (exp.f64 a)))
97.0ms	(+.f64 (exp.f64 a) 1)
46.0ms	(/.f64 1 (+.f64 (exp.f64 a) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	99	6
2	1092	6
3	4678	6
4	5027	6
0	6	9
1	125	9
2	1408	9
3	5307	9
0	9	17
1	179	16
2	2041	16
3	5024	16

simplify98.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

670×	`sub-neg_binary64`
475×	`associate-+l+_binary64`
414×	`associate--r+_binary64`
353×	`associate-l_binary64`
333×	`associate-+r+_binary64`

Counts

171 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	591
1	151	582
2	411	567
3	1214	565
4	2798	565
5	4607	565
6	4960	565
7	5386	565

prune127.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	146	6	152

Error

1.2b

Counts

152 → 6

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (-.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 1))
	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))))
✓	2.2b	(fma.f64 (/.f64 1 (+.f64 (exp.f64 a) 1)) b (log1p.f64 (exp.f64 a)))
▶	2.9b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2) (log1p.f64 (exp.f64 a)))
	28.4b	(fma.f64 1/2 b (log1p.f64 (exp.f64 a)))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))

Compiler

Compiled 2543 to 1439 computations (43.4% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) 1)
✓	0.2b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2) (log1p.f64 (exp.f64 a)))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2)
✓	0.6b	(cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1)))

series2.9s (14.1%)

Counts

3 → 72

Calls

3 calls:

1.8s

(fma.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2) (log1p.f64 (exp.f64 a)))

545.0ms

(pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2)

520.0ms

(cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1)))

rewrite161.0ms (0.8%)

Algorithm

3×	egg-rewrite

Rules

59×	`egg`
29×	`egg`
26×	`egg`

Counts

3 → 114

Calls

3 calls:

58.0ms

(fma.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2) (log1p.f64 (exp.f64 a)))

52.0ms

(pow.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) 2)

49.0ms

(cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	162	11
2	1967	11
3	5085	11
0	10	14
1	205	12
2	2260	12
3	5460	12
0	12	32
1	240	16
2	2656	16
3	5035	16

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
707×	`unswap-sqr_binary64`
421×	`associate-r_binary64`
402×	`associate-l_binary64`
319×	`fma-def_binary64`

Counts

186 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1721
1	309	1620
2	864	1489
3	3347	1239
4	5868	1239

prune285.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	314	2	316
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	316	6	322

Error

1.2b

Counts

322 → 6

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (-.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 1))
	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))))
✓	2.2b	(fma.f64 (/.f64 1 (+.f64 (exp.f64 a) 1)) b (log1p.f64 (exp.f64 a)))
	28.4b	(fma.f64 1/2 b (log1p.f64 (exp.f64 a)))
	3.7b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))))) 2) (log1p.f64 (exp.f64 a)))
	3.4b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1))) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 (exp.f64 a) 1)))) 3) 2) (log1p.f64 (exp.f64 a)))

Compiler

Compiled 7773 to 4608 computations (40.7% saved)

regimes334.0ms (1.6%)

Accuracy

Total 0.6b remaining (52.1%)

Threshold costs 0.6b (52.1%)

Counts

72 → 1

Compiler

Compiled 6037 to 4428 computations (26.7% 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

end243.0ms (1.2%)

Compiler: Compiled 150 to 108 computations (28% saved)

Details

analyze779.0ms (3.8%)

sample13.1s (64.6%)

simplify5.0ms (0%)

prune2.0ms (0%)

localize9.0ms (0%)

series437.0ms (2.1%)

rewrite164.0ms (0.8%)

simplify82.0ms (0.4%)

prune58.0ms (0.3%)

localize6.0ms (0%)

series265.0ms (1.3%)

rewrite265.0ms (1.3%)

simplify99.0ms (0.5%)

prune136.0ms (0.7%)

localize7.0ms (0%)

series358.0ms (1.8%)

rewrite317.0ms (1.6%)

simplify98.0ms (0.5%)

prune127.0ms (0.6%)

localize10.0ms (0%)

series2.9s (14.1%)

rewrite161.0ms (0.8%)

simplify81.0ms (0.4%)

prune285.0ms (1.4%)

regimes334.0ms (1.6%)

simplify2.0ms (0%)

end243.0ms (1.2%)

Profiling