Details

analyze821.0ms (15.9%)

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 (22.4%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

886.0ms	8256×	body	128	valid
224.0ms	1984×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify8.0ms (0.1%)

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

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

10.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.3b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series32.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

32.0ms

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

rewrite5.0ms (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:

4.0ms

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

simplify87.0ms (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

prune31.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	27	9	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	9	37

Error

0.1b

Counts

37 → 9

Alt Table

Status	Error	Program
	10.4b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	28.0b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
	40.7b	(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))))
	11.0b	(.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))))
	11.0b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	9.7b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	13.5b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	11.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

Compiler

Compiled 744 to 261 computations (64.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.0b	(/.f64 (*.f64 a1 a2) b1)
✓	5.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

series42.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
13.0ms	(/.f64 (*.f64 a1 a2) b1)

rewrite13.0ms (0.2%)

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:

5.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
4.0ms	(/.f64 (*.f64 a1 a2) b1)

simplify101.0ms (1.9%)

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

prune81.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Error

Counts

109 → 10

Alt Table

Status	Error	Program
▶	9.5b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	22.1b	(.f64 (/.f64 1 (sqrt.f64 b2)) (/.f64 (/.f64 (.f64 a1 a2) b1) (sqrt.f64 b2)))
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.4b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	10.2b	(.f64 (/.f64 (.f64 a1 a2) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 1 b1) (cbrt.f64 b2)))
	10.3b	(.f64 1 (/.f64 (.f64 a1 a2) (*.f64 b2 b1)))
	9.7b	(/.f64 (/.f64 1 (/.f64 b1 (*.f64 a1 a2))) b2)
	10.7b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	13.5b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	11.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

Compiler

Compiled 1616 to 495 computations (69.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.0b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
✓	5.0b	(*.f64 a1 (/.f64 a2 b1))

series41.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

28.0ms	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
12.0ms	(*.f64 a1 (/.f64 a2 b1))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms	(*.f64 a1 (/.f64 a2 b1))
4.0ms	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)

simplify100.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

876×	`times-frac_binary64`
547×	`associate-/l/_binary64`
515×	`associate-*l/_binary64`
432×	`associate-*r/_binary64`
360×	`associate-l_binary64`

Counts

144 → 88

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	110	1520
1	267	1391
2	1002	1391
3	3995	1391
4	4305	1391
5	4887	1391
6	4957	1391

prune55.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	88	10	98

Error

Counts

98 → 10

Alt Table

Status	Error	Program
	9.8b	(/.f64 1 (/.f64 b2 (*.f64 a1 (/.f64 a2 b1))))
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.4b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	10.2b	(.f64 (/.f64 (.f64 a1 a2) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 1 b1) (cbrt.f64 b2)))
	10.3b	(.f64 1 (/.f64 (.f64 a1 a2) (*.f64 b2 b1)))
▶	9.7b	(/.f64 (/.f64 1 (/.f64 b1 (*.f64 a1 a2))) b2)
✓	9.5b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	10.7b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	13.5b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	11.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

Compiler

Compiled 1359 to 461 computations (66.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 b1 (*.f64 a1 a2)))
✓	4.9b	(/.f64 b1 (*.f64 a1 a2))
✓	5.0b	(/.f64 (/.f64 1 (/.f64 b1 (*.f64 a1 a2))) b2)

series58.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

29.0ms	(/.f64 (/.f64 1 (/.f64 b1 (*.f64 a1 a2))) b2)
17.0ms	(/.f64 b1 (*.f64 a1 a2))
12.0ms	(/.f64 1 (/.f64 b1 (*.f64 a1 a2)))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64`
104×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
61×	`add-exp-log_binary64`

Counts

3 → 215

Calls

3 calls:

9.0ms	(/.f64 (/.f64 1 (/.f64 b1 (*.f64 a1 a2))) b2)
5.0ms	(/.f64 1 (/.f64 b1 (*.f64 a1 a2)))
3.0ms	(/.f64 b1 (*.f64 a1 a2))

simplify179.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

627×	`associate-/r/_binary64`
452×	`associate-*l/_binary64`
403×	`fma-def_binary64`
396×	`associate-l_binary64`
333×	`fma-neg_binary64`

Counts

299 → 286

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	4861
1	426	4237
2	1316	4129
3	3082	4129
4	4032	4129
5	4520	4129
6	5158	4129

prune175.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	287	9	296

Error

Counts

296 → 9

Alt Table

Status	Error	Program
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.9b	(/.f64 (/.f64 1 (/.f64 (/.f64 b1 a1) a2)) b2)
	10.4b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	9.7b	(/.f64 1 (.f64 b2 (/.f64 b1 (.f64 a1 a2))))
	10.2b	(.f64 (/.f64 (.f64 a1 a2) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 1 b1) (cbrt.f64 b2)))
	10.3b	(.f64 1 (/.f64 (.f64 a1 a2) (*.f64 b2 b1)))
✓	9.5b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	10.7b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

Compiler

Compiled 5138 to 2043 computations (60.2% saved)

regimes1.7s (33.4%)

Accuracy

Total 2.5b remaining (99.3%)

Threshold costs 0b (0%)

Counts

79 → 5

Compiler

Compiled 10484 to 6182 computations (41% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	149
1	43	149
2	42	149

end377.0ms (7.3%)

Compiler: Compiled 730 to 288 computations (60.5% saved)

Details

analyze821.0ms (15.9%)

sample1.2s (22.4%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series32.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify87.0ms (1.7%)

prune31.0ms (0.6%)

localize5.0ms (0.1%)

series42.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify101.0ms (1.9%)

prune81.0ms (1.6%)

localize5.0ms (0.1%)

series41.0ms (0.8%)

rewrite12.0ms (0.2%)

simplify100.0ms (1.9%)

prune55.0ms (1.1%)

localize6.0ms (0.1%)

series58.0ms (1.1%)

rewrite35.0ms (0.7%)

simplify179.0ms (3.5%)

prune175.0ms (3.4%)

regimes1.7s (33.4%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end377.0ms (7.3%)

Profiling