Details

analyze1.8s (21.8%)

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)

sample2.3s (28.2%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

1.8s	8256×	body	128	valid
418.0ms	1848×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify18.0ms (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

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

10.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series72.0ms (0.9%)

Counts

1 → 48

Calls

1 calls:

71.0ms

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

rewrite12.0ms (0.1%)

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:

9.0ms

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

simplify143.0ms (1.7%)

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

prune53.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	7	37

Error

0.0b

Counts

37 → 7

Alt Table

Status	Error	Program
▶	10.6b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	13.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	11.1b	(.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))))
	11.7b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	14.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.5b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

Compiler

Compiled 646 to 219 computations (66.1% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
✓	10.1b	(/.f64 (.f64 b1 b2) (.f64 a1 a2))

series124.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

63.0ms	(/.f64 (.f64 b1 b2) (.f64 a1 a2))
61.0ms	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
26×	`div-exp_binary64`
20×	`times-frac_binary64`
16×	`prod-exp_binary64`

Counts

2 → 81

Calls

2 calls:

12.0ms	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
9.0ms	(/.f64 (.f64 b1 b2) (.f64 a1 a2))

simplify176.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-*l/_binary64`
648×	`associate-l_binary64`
526×	`associate-*r/_binary64`
496×	`associate-/l/_binary64`
461×	`associate-/r/_binary64`

Counts

177 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	2403
1	226	2062
2	1133	2041
3	4579	2041
4	4937	2041
5	5030	2041

prune140.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	110	10	120

Error

0.0b

Counts

120 → 10

Alt Table

Status	Error	Program
	11.3b	(/.f64 (/.f64 1 (.f64 b1 b2)) (/.f64 1 (.f64 a1 a2)))
✓	10.6b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	13.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	13.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	13.7b	(/.f64 (/.f64 1 (/.f64 b1 a1)) (/.f64 b2 a2))
	11.7b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a1) a2))
▶	10.6b	(/.f64 1 (.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2))))
	11.7b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	14.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

Compiler

Compiled 1978 to 698 computations (64.7% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (*.f64 a1 a2))
✓	0.4b	(/.f64 1 (.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2))))
✓	10.1b	(.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2)))

series139.0ms (1.7%)

Counts

3 → 96

Calls

3 calls:

61.0ms	(/.f64 1 (.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2))))
61.0ms	(.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2)))
17.0ms	(/.f64 1 (*.f64 a1 a2))

rewrite72.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

212×	`add-exp-log_binary64`
111×	`prod-exp_binary64`
66×	`div-exp_binary64`
58×	`add-cbrt-cube_binary64`
33×	`rec-exp_binary64`

Counts

3 → 149

Calls

3 calls:

17.0ms	(/.f64 1 (.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2))))
16.0ms	(.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2)))
6.0ms	(/.f64 1 (*.f64 a1 a2))

simplify249.0ms (3%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-/l*_binary64`
597×	`associate-/r*_binary64`
547×	`associate-*l/_binary64`
353×	`associate-/l/_binary64`
326×	`associate-/r/_binary64`

Counts

245 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	135	3075
1	275	2524
2	1046	2524
3	4407	2524
4	4924	2524
5	4995	2524
6	4995	2524

prune198.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	175	10	185

Error

0.0b

Counts

185 → 10

Alt Table

Status	Error	Program
	11.3b	(/.f64 (/.f64 1 (.f64 b1 b2)) (/.f64 1 (.f64 a1 a2)))
✓	10.6b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	13.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	13.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	13.7b	(/.f64 (/.f64 1 (/.f64 b1 a1)) (/.f64 b2 a2))
	11.7b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a1) a2))
✓	10.6b	(/.f64 1 (.f64 (.f64 b1 b2) (/.f64 1 (*.f64 a1 a2))))
	11.7b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	14.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

Compiler

Compiled 3061 to 1407 computations (54% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.5b	(/.f64 (*.f64 a1 a2) b1)
✓	6.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

series86.0ms (1%)

Counts

2 → 48

Calls

2 calls:

60.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
26.0ms	(/.f64 (*.f64 a1 a2) b1)

rewrite26.0ms (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:

10.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
6.0ms	(/.f64 (*.f64 a1 a2) b1)

simplify168.0ms (2%)

Algorithm

1×	egg-herbie

Rules

821×	`associate-/l*_binary64`
608×	`associate-/l/_binary64`
389×	`associate-*l/_binary64`
362×	`associate-/r*_binary64`
291×	`associate-*r/_binary64`

Counts

121 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	127	1639
1	304	1510
2	967	1510
3	4038	1510
4	4410	1510
5	4842	1510
6	5018	1510

prune116.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	5	7
Picked	0	1	1
Done	2	0	2
Total	102	8	110

Error

Counts

110 → 8

Alt Table

Status	Error	Program
	13.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	13.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	13.7b	(/.f64 (/.f64 1 (/.f64 b1 a1)) (/.f64 b2 a2))
	10.5b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	11.7b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a1) a2))
	10.5b	(/.f64 (*.f64 a1 a2) (/.f64 b2 (/.f64 1 b1)))
✓	11.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	14.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

Compiler

Compiled 1444 to 383 computations (73.5% saved)

regimes1.2s (15%)

Accuracy

Total 3.2b remaining (99.3%)

Threshold costs 0b (0%)

Counts

35 → 5

Compiler

Compiled 4858 to 2756 computations (43.3% saved)

bsearch2.0ms (0%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	110
1	31	110
2	31	110

end1.0s (12.2%)

Compiler: Compiled 568 to 212 computations (62.7% saved)

Details

analyze1.8s (21.8%)

sample2.3s (28.2%)

simplify18.0ms (0.2%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series72.0ms (0.9%)

rewrite12.0ms (0.1%)

simplify143.0ms (1.7%)

prune53.0ms (0.6%)

localize14.0ms (0.2%)

series124.0ms (1.5%)

rewrite34.0ms (0.4%)

simplify176.0ms (2.1%)

prune140.0ms (1.7%)

localize17.0ms (0.2%)

series139.0ms (1.7%)

rewrite72.0ms (0.9%)

simplify249.0ms (3%)

prune198.0ms (2.4%)

localize11.0ms (0.1%)

series86.0ms (1%)

rewrite26.0ms (0.3%)

simplify168.0ms (2%)

prune116.0ms (1.4%)

regimes1.2s (15%)

bsearch2.0ms (0%)

simplify8.0ms (0.1%)

end1.0s (12.2%)

Profiling