Details

analyze725.0ms (18.8%)

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)

sample52.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

9.0ms	256×	body	128	valid
5.0ms	55×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify7.0ms (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

10.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.8b	(/.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
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series33.0ms (0.9%)

Counts

1 → 48

Calls

1 calls:

33.0ms

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

rewrite6.0ms (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))

simplify89.0ms (2.3%)

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

prune29.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	6	37

Error

0.0b

Counts

37 → 6

Alt Table

Status	Error	Program
	12.8b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
▶	9.5b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.2b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	10.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	29.3b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 606 to 203 computations (66.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.8b	(/.f64 (*.f64 b1 b2) a2)
✓	6.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

series42.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

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

rewrite12.0ms (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:

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

simplify76.0ms (2%)

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

prune74.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	120	7	127

Error

Counts

127 → 7

Alt Table

Status	Error	Program
	10.6b	(.f64 (/.f64 (.f64 (cbrt.f64 a2) (cbrt.f64 a2)) b1) (/.f64 a1 (/.f64 b2 (cbrt.f64 a2))))
	12.8b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	10.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
▶	9.1b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.3b	(.f64 (/.f64 1 (.f64 b1 b2)) (/.f64 a1 (/.f64 1 a2)))
	10.9b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))

Compiler

Compiled 1807 to 496 computations (72.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.1b	(/.f64 a2 (*.f64 b2 b1))
✓	5.7b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))

series46.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
17.0ms	(/.f64 a2 (*.f64 b2 b1))

rewrite11.0ms (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:

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

simplify101.0ms (2.6%)

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

prune35.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Error

Counts

73 → 7

Alt Table

Status	Error	Program
	12.8b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	12.4b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
▶	10.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	9.1b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.3b	(.f64 (/.f64 1 (.f64 b1 b2)) (/.f64 a1 (/.f64 1 a2)))
	10.9b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))

Compiler

Compiled 987 to 307 computations (68.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series32.0ms (0.8%)

Counts

1 → 48

Calls

1 calls:

32.0ms

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

rewrite13.0ms (0.3%)

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:

10.0ms

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

simplify124.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

648×	`associate-*l/_binary64`
573×	`associate-*r/_binary64`
489×	`associate-l_binary64`
469×	`associate-/l*_binary64`
389×	`associate-r_binary64`

Counts

100 → 81

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	113	1295
1	308	1187
2	960	1187
3	3807	1187
4	4046	1187
5	4634	1187
6	4940	1187
7	4956	1187
8	4976	1187

prune39.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	81	7	88

Error

Counts

88 → 7

Alt Table

Status	Error	Program
	11.0b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)
	12.8b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.4b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	10.5b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	9.1b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.3b	(.f64 (/.f64 1 (.f64 b1 b2)) (/.f64 a1 (/.f64 1 a2)))
	10.9b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))

Compiler

Compiled 1241 to 324 computations (73.9% saved)

regimes1.2s (30.9%)

Accuracy

Total 2.2b remaining (99.1%)

Threshold costs 0b (0%)

Counts

60 → 5

Compiler

Compiled 7879 to 4504 computations (42.8% 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`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	137
1	45	137
2	44	137

end30.0ms (0.8%)

Compiler: Compiled 475 to 180 computations (62.1% saved)

sample1.1s (27.5%)

Algorithm

1×

intervals

Results

309.0ms	8000×	body	128	valid
64.0ms	1773×	body	128	invalid

Compiler

Compiled 194 to 103 computations (46.9% saved)

Details

analyze725.0ms (18.8%)

sample52.0ms (1.3%)

simplify7.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series33.0ms (0.9%)

rewrite6.0ms (0.1%)

simplify89.0ms (2.3%)

prune29.0ms (0.8%)

localize5.0ms (0.1%)

series42.0ms (1.1%)

rewrite12.0ms (0.3%)

simplify76.0ms (2%)

prune74.0ms (1.9%)

localize5.0ms (0.1%)

series46.0ms (1.2%)

rewrite11.0ms (0.3%)

simplify101.0ms (2.6%)

prune35.0ms (0.9%)

localize5.0ms (0.1%)

series32.0ms (0.8%)

rewrite13.0ms (0.3%)

simplify124.0ms (3.2%)

prune39.0ms (1%)

regimes1.2s (30.9%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end30.0ms (0.8%)

sample1.1s (27.5%)

Profiling