Details

analyze768.0ms (3.7%)

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)

sample12.8s (62.5%)

Symmetry

(sort a b)

Results

10.0s	7975×	body	8192	exit
1.4s	1995×	body	1024	valid
605.0ms	4582×	body	128	valid
434.0ms	1028×	body	512	valid
186.0ms	207×	body	2048	valid
124.0ms	444×	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

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)

localize6.0ms (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)))

series679.0ms (3.3%)

Counts

2 → 48

Calls

2 calls:

675.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite48.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

58× egg-rr

Counts

2 → 58

Calls

2 calls:

47.0ms	((log.f64 (+.f64 (exp.f64 a) (exp.f64 b))) (+.f64 (exp.f64 a) (exp.f64 b)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	137	18
2	1701	18
3	4952	18
0	0	0
1	0	0

simplify66.0ms (0.3%)

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

106 → 89

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

prune55.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Error

1.2b

Counts

90 → 3

Alt Table

Status	Error	Program
▶	2.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	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))

Compiler

Compiled 1435 to 719 computations (49.9% saved)

localize8.0ms (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))

series274.0ms (1.3%)

Counts

3 → 32

Calls

3 calls:

252.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
20.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite94.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

123× egg-rr

Counts

3 → 123

Calls

2 calls:

92.0ms	((+.f64 1 (exp.f64 a)) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	187	31
2	2486	31
3	4739	31
4	5016	31
0	0	0
1	0	0

simplify86.0ms (0.4%)

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

155 → 149

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

prune130.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	147	5	152

Error

1.2b

Counts

152 → 5

Alt Table

Status	Error	Program
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
▶	2.9b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) 2) (log1p.f64 (exp.f64 a)))
	30.2b	(log1p.f64 (-.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 1))
	30.7b	(fma.f64 (/.f64 b (-.f64 1 (pow.f64 (exp.f64 a) 2))) (-.f64 1 (exp.f64 a)) (log1p.f64 (exp.f64 a)))

Compiler

Compiled 2623 to 1394 computations (46.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.8s (13.9%)

Counts

3 → 72

Calls

3 calls:

1.6s

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

642.0ms

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

555.0ms

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

rewrite71.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

86× egg-rr

Counts

3 → 86

Calls

2 calls:

69.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	57
1	239	39
2	2683	39
3	5152	39
0	0	0
1	0	0

simplify71.0ms (0.3%)

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

158 → 127

Iterations

Useful iterations: 3 (0.0ms)

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

prune214.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	256	2	258
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	258	5	263

Error

1.2b

Counts

263 → 5

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (-.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 1))
	3.7b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))) 2) (log1p.f64 (exp.f64 a)))
	3.4b	(fma.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) 3) 2) (log1p.f64 (exp.f64 a)))
▶	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	30.7b	(fma.f64 (/.f64 b (-.f64 1 (pow.f64 (exp.f64 a) 2))) (-.f64 1 (exp.f64 a)) (log1p.f64 (exp.f64 a)))

Compiler

Compiled 6567 to 3973 computations (39.5% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	0.1b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

series915.0ms (4.5%)

Counts

2 → 48

Calls

2 calls:

654.0ms	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
260.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

rewrite118.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

59× egg-rr

Counts

2 → 59

Calls

2 calls:

116.0ms	((expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	206	34
2	2678	34
3	4991	34
4	4602	34
5	4996	34
0	0	0
1	0	0

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

426×	`associate-+r+_binary64`
269×	`associate-+l+_binary64`
267×	`+-commutative_binary64`
226×	`cancel-sign-sub-inv_binary64`
216×	`times-frac_binary64`

Counts

107 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	2850
1	860	2775
2	3707	2714
3	4925	2714
4	4978	2714

prune175.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	190	4	194

Error

1.2b

Counts

194 → 4

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (-.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 1))
	62.9b	(expm1.f64 (-.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log.f64 (+.f64 1 (exp.f64 a))) b) (/.f64 (*.f64 (log.f64 (+.f64 1 (exp.f64 a))) (exp.f64 a)) b))))) (log.f64 (/.f64 1 b))))
	3.0b	(expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))))))
	30.7b	(fma.f64 (/.f64 b (-.f64 1 (pow.f64 (exp.f64 a) 2))) (-.f64 1 (exp.f64 a)) (log1p.f64 (exp.f64 a)))

Compiler

Compiled 6095 to 3669 computations (39.8% saved)

regimes733.0ms (3.6%)

Accuracy

Total 0.5b remaining (52.1%)

Threshold costs 0.5b (52.1%)

Counts

157 → 1

Compiler

Compiled 14011 to 10064 computations (28.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	11	28
2	11	28

end226.0ms (1.1%)

Compiler: Compiled 159 to 97 computations (39% saved)

Details

analyze768.0ms (3.7%)

sample12.8s (62.5%)

simplify6.0ms (0%)

prune2.0ms (0%)

localize6.0ms (0%)

series679.0ms (3.3%)

rewrite48.0ms (0.2%)

simplify66.0ms (0.3%)

prune55.0ms (0.3%)

localize8.0ms (0%)

series274.0ms (1.3%)

rewrite94.0ms (0.5%)

simplify86.0ms (0.4%)

prune130.0ms (0.6%)

localize11.0ms (0.1%)

series2.8s (13.9%)

rewrite71.0ms (0.3%)

simplify71.0ms (0.3%)

prune214.0ms (1%)

localize9.0ms (0%)

series915.0ms (4.5%)

rewrite118.0ms (0.6%)

simplify99.0ms (0.5%)

prune175.0ms (0.9%)

regimes733.0ms (3.6%)

simplify4.0ms (0%)

end226.0ms (1.1%)

Profiling