Details

analyze862.0ms (19%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	81.1%	0.2%	9
21.8%	78%	0.2%	10
25%	74.9%	0.2%	11
34.7%	64.9%	0.4%	12
47.2%	51.9%	0.9%	13
49%	49.2%	1.8%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.2s (26.1%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

941.0ms	8256×	body	128	valid
198.0ms	1867×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
9×	`associate-/r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	38	10
3	63	10
4	69	10
5	68	10
6	68	10

prune1.0ms (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

12.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.9b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	12.6b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series32.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

32.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
4×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_binary64`

Counts

1 → 23

Calls

1 calls:

10.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/r*_binary64`
476×	`associate-l_binary64`
457×	`associate-*l/_binary64`
355×	`associate-*r/_binary64`
344×	`associate-r_binary64`

Counts

71 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	58	859
1	161	754
2	820	754
3	3799	754
4	4127	754
5	4478	754
6	4861	754
7	5308	754

prune32.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	8	37

Error

0.1b

Counts

37 → 8

Alt Table

Status	Error	Program
	12.9b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	12.9b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	10.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
▶	10.6b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	10.9b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	41.3b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 a1 a2) (.f64 a1 a2)) (.f64 a1 a2)) (.f64 (.f64 (.f64 b1 b2) (.f64 b1 b2)) (.f64 b1 b2))))
	13.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2)))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))))

Compiler

Compiled 687 to 232 computations (66.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.7b	(/.f64 (*.f64 b1 b2) a2)
✓	6.2b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

series52.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

38.0ms	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
14.0ms	(/.f64 (*.f64 b1 b2) a2)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

4.0ms	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
3.0ms	(/.f64 (*.f64 b1 b2) a2)

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
673×	`associate-/l*_binary64`
506×	`associate-/l/_binary64`
500×	`associate-*l/_binary64`
480×	`associate-/r/_binary64`

Counts

157 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1914
1	291	1782
2	1078	1770
3	4951	1770
4	5016	1770

prune92.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	5	1	6
Picked	0	1	1
Done	1	0	1
Total	120	9	129

Error

0.0b

Counts

129 → 9

Alt Table

Status	Error	Program
	10.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	10.7b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	11.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (.f64 b1 b2) a2)) (cbrt.f64 (/.f64 (.f64 b1 b2) a2)))) (/.f64 a1 (cbrt.f64 (/.f64 (*.f64 b1 b2) a2))))
▶	10.2b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
✓	10.6b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	13.0b	(/.f64 1 (/.f64 b1 (/.f64 a1 (/.f64 b2 a2))))
	13.1b	(.f64 (/.f64 1 (.f64 b1 b2)) (/.f64 a1 (/.f64 1 a2)))
	12.5b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))
	21.6b	(/.f64 (/.f64 a1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 b2 (sqrt.f64 a2)))

Compiler

Compiled 1872 to 529 computations (71.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.7b	(/.f64 a2 (*.f64 b2 b1))
✓	5.7b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))

series44.0ms (1%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
16.0ms	(/.f64 a2 (*.f64 b2 b1))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

6.0ms	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
3.0ms	(/.f64 a2 (*.f64 b2 b1))

simplify102.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

760×	`times-frac_binary64`
492×	`associate-l_binary64`
425×	`associate-*r/_binary64`
417×	`associate-*l/_binary64`
415×	`associate-r_binary64`

Counts

100 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	83	1170
1	194	1041
2	738	1041
3	3961	1041
4	4334	1041
5	4876	1041
6	4978	1041
7	4997	1041

prune49.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Error

0.0b

Counts

75 → 9

Alt Table

Status	Error	Program
	10.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	10.7b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
▶	10.0b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	10.2b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
✓	10.6b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	13.0b	(/.f64 1 (/.f64 b1 (/.f64 a1 (/.f64 b2 a2))))
	13.1b	(.f64 (/.f64 1 (.f64 b1 b2)) (/.f64 a1 (/.f64 1 a2)))
	12.5b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))
	21.6b	(/.f64 (/.f64 a1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 b2 (sqrt.f64 a2)))

Compiler

Compiled 1032 to 336 computations (67.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.8b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))

series28.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

28.0ms

(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

1 → 52

Calls

1 calls:

7.0ms

(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))

simplify118.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-*l/_binary64`
544×	`associate-*r/_binary64`
468×	`associate-/l*_binary64`
436×	`associate-l_binary64`
346×	`associate-r_binary64`

Counts

100 → 80

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	1295
1	305	1187
2	936	1187
3	3638	1187
4	3888	1187
5	4481	1187
6	4834	1187
7	4979	1187
8	5014	1187

prune42.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	80	9	89

Error

Counts

89 → 9

Alt Table

Status	Error	Program
	10.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	10.7b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	9.9b	(/.f64 (*.f64 (/.f64 a1 b2) a2) b1)
	21.6b	(/.f64 (/.f64 a1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 b2 (sqrt.f64 a2)))
✓	10.0b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	10.2b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
✓	10.6b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	13.0b	(/.f64 1 (/.f64 b1 (/.f64 a1 (/.f64 b2 a2))))
	12.5b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))

Compiler

Compiled 1258 to 336 computations (73.3% saved)

regimes1.3s (27.6%)

Accuracy

Total 2.3b remaining (99.5%)

Threshold costs 0b (0%)

Counts

72 → 5

Compiler

Compiled 9202 to 5263 computations (42.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	113
1	39	113
2	38	113

end395.0ms (8.7%)

Compiler: Compiled 593 to 243 computations (59% saved)

Details

analyze862.0ms (19%)

sample1.2s (26.1%)

simplify10.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series32.0ms (0.7%)

rewrite11.0ms (0.2%)

simplify88.0ms (2%)

prune32.0ms (0.7%)

localize5.0ms (0.1%)

series52.0ms (1.2%)

rewrite14.0ms (0.3%)

simplify77.0ms (1.7%)

prune92.0ms (2%)

localize6.0ms (0.1%)

series44.0ms (1%)

rewrite12.0ms (0.3%)

simplify102.0ms (2.2%)

prune49.0ms (1.1%)

localize6.0ms (0.1%)

series28.0ms (0.6%)

rewrite11.0ms (0.2%)

simplify118.0ms (2.6%)

prune42.0ms (0.9%)

regimes1.3s (27.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end395.0ms (8.7%)

Profiling