Details

analyze721.0ms (14%)

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)

sample50.0ms (1%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

9.0ms	256×	body	128	valid
2.0ms	53×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify7.0ms (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

12.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.8b	(/.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
✓	12.4b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series29.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

28.0ms

(/.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))

simplify86.0ms (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

prune29.0ms (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
	12.8b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	13.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	34.5b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
	13.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	11.4b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	13.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.7b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

Compiler

Compiled 628 to 217 computations (65.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.9b	(/.f64 (*.f64 a1 a2) b1)
✓	8.3b	(/.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)

rewrite12.0ms (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)
3.0ms	(/.f64 (*.f64 a1 a2) b1)

simplify98.0ms (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

prune70.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	99	8	107

Error

Counts

107 → 8

Alt Table

Status	Error	Program
	12.1b	(*.f64 (/.f64 (/.f64 a1 1) 1) (/.f64 (/.f64 a2 b1) b2))
	13.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	13.5b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	12.2b	(/.f64 (/.f64 a1 1) (/.f64 b2 (/.f64 a2 b1)))
▶	11.4b	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
✓	11.4b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	20.1b	(.f64 (/.f64 (.f64 a1 a2) (sqrt.f64 b2)) (/.f64 (/.f64 1 b1) (sqrt.f64 b2)))
	12.3b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)

Compiler

Compiled 1543 to 450 computations (70.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
	3.9b	(/.f64 (*.f64 a1 a2) b1)
✓	8.2b	(/.f64 b2 (/.f64 (*.f64 a1 a2) b1))

series56.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

29.0ms	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
27.0ms	(/.f64 b2 (/.f64 (*.f64 a1 a2) b1))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

231×	`times-frac_binary64`
101×	`*-un-lft-identity_binary64`
101×	`add-sqr-sqrt_binary64`
101×	`add-cube-cbrt_binary64`
45×	`add-exp-log_binary64`

Counts

2 → 188

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
4.0ms	(/.f64 b2 (/.f64 (*.f64 a1 a2) b1))

simplify213.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-neg_binary64`
742×	`fma-def_binary64`
381×	`*-commutative_binary64`
331×	`sqr-pow_binary64`
200×	`associate-/r/_binary64`

Counts

284 → 272

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	4864
1	400	4385
2	1515	4268
3	2200	4268
4	3262	4268
5	3933	4268
6	4640	4268
7	4934	4268

prune168.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	3	3	6
Picked	0	1	1
Done	1	0	1
Total	301	7	308

Error

Counts

308 → 7

Alt Table

Status	Error	Program
	12.2b	(/.f64 a1 (/.f64 b2 (/.f64 a2 b1)))
✓	11.4b	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
	13.5b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
▶	12.1b	(*.f64 a1 (/.f64 (/.f64 a2 b1) b2))
	12.2b	(/.f64 (/.f64 a2 (/.f64 b2 a1)) b1)
	20.1b	(.f64 (/.f64 (.f64 a1 a2) (sqrt.f64 b2)) (/.f64 (/.f64 1 b1) (sqrt.f64 b2)))
	12.3b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)

Compiler

Compiled 5403 to 1727 computations (68% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.3b	(/.f64 (/.f64 a2 b1) b2)
✓	8.4b	(*.f64 a1 (/.f64 (/.f64 a2 b1) b2))

series42.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

26.0ms	(*.f64 a1 (/.f64 (/.f64 a2 b1) b2))
16.0ms	(/.f64 (/.f64 a2 b1) b2)

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
89×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
80×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

2 → 139

Calls

2 calls:

12.0ms	(*.f64 a1 (/.f64 (/.f64 a2 b1) b2))
4.0ms	(/.f64 (/.f64 a2 b1) b2)

simplify160.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-/r/_binary64`
482×	`fma-neg_binary64`
468×	`associate-/r*_binary64`
287×	`*-commutative_binary64`
177×	`sqr-pow_binary64`

Counts

223 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	218	3063
1	516	2916
2	1658	2916
3	2591	2916
4	3302	2916
5	3748	2916
6	4589	2916
7	5076	2916

prune94.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	201	7	208

Error

Counts

208 → 7

Alt Table

Status	Error	Program
	12.2b	(/.f64 a1 (/.f64 b2 (/.f64 a2 b1)))
✓	11.4b	(/.f64 1 (/.f64 b2 (/.f64 (*.f64 a1 a2) b1)))
	13.5b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
✓	12.1b	(*.f64 a1 (/.f64 (/.f64 a2 b1) b2))
	12.2b	(/.f64 (/.f64 a2 (/.f64 b2 a1)) b1)
	20.1b	(.f64 (/.f64 (.f64 a1 a2) (sqrt.f64 b2)) (/.f64 (/.f64 1 b1) (sqrt.f64 b2)))
	12.3b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)

Compiler

Compiled 3313 to 808 computations (75.6% saved)

regimes1.9s (37.5%)

Accuracy

Total 2.9b remaining (99%)

Threshold costs 0b (0%)

Counts

87 → 5

Compiler

Compiled 10746 to 6542 computations (39.1% 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×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	146
1	43	146
2	42	146

end27.0ms (0.5%)

Compiler: Compiled 500 to 165 computations (67% saved)

sample1.2s (23.7%)

Algorithm

1×

intervals

Results

387.0ms	8000×	body	128	valid
68.0ms	1897×	body	128	invalid

Compiler

Compiled 201 to 100 computations (50.2% saved)

Details

analyze721.0ms (14%)

sample50.0ms (1%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series29.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify86.0ms (1.7%)

prune29.0ms (0.6%)

localize7.0ms (0.1%)

series42.0ms (0.8%)

rewrite12.0ms (0.2%)

simplify98.0ms (1.9%)

prune70.0ms (1.4%)

localize8.0ms (0.2%)

series56.0ms (1.1%)

rewrite32.0ms (0.6%)

simplify213.0ms (4.1%)

prune168.0ms (3.3%)

localize5.0ms (0.1%)

series42.0ms (0.8%)

rewrite28.0ms (0.5%)

simplify160.0ms (3.1%)

prune94.0ms (1.8%)

regimes1.9s (37.5%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end27.0ms (0.5%)

sample1.2s (23.7%)

Profiling