Details

analyze683.0ms (12.3%)

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)

sample54.0ms (1%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

11.0ms	256×	body	128	valid
2.0ms	62×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% 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

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

12.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.2b	(/.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
✓	11.9b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series35.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

35.0ms

(/.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))

simplify85.0ms (1.5%)

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 (0.6%)

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
	12.0b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	32.5b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
	12.8b	(.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))))
	13.4b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	10.7b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	11.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.4b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	12.4b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.4b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))

Compiler

Compiled 714 to 255 computations (64.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.7b	(/.f64 (*.f64 a1 a2) b1)
✓	8.1b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

series41.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.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)
3.0ms	(/.f64 (*.f64 a1 a2) b1)

simplify96.0ms (1.7%)

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

prune75.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Error

Counts

109 → 8

Alt Table

Status	Error	Program
	11.9b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
▶	11.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.7b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	13.7b	(*.f64 (/.f64 (/.f64 a1 1) 1) (/.f64 (/.f64 a2 b1) b2))
	28.0b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) (sqrt.f64 b2)) (sqrt.f64 b2))
	12.5b	(/.f64 (/.f64 a1 (*.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 b2 (/.f64 a2 (cbrt.f64 b1))))
	13.4b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 1564 to 459 computations (70.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.0b	(/.f64 b1 (/.f64 a2 b2))
✓	9.0b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

series40.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

27.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
13.0ms	(/.f64 b1 (/.f64 a2 b2))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`times-frac_binary64`
229×	`*-un-lft-identity_binary64`
229×	`add-sqr-sqrt_binary64`
229×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

2 → 270

Calls

2 calls:

10.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
4.0ms	(/.f64 b1 (/.f64 a2 b2))

simplify284.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

558×	`associate-/r/_binary64`
413×	`associate-/l/_binary64`
375×	`associate-*l/_binary64`
330×	`*-commutative_binary64`
328×	`associate-*r/_binary64`

Counts

354 → 449

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	452	7123
1	994	6901
2	3658	6898
3	3582	6898
4	4211	6898
5	4604	6898
6	5079	6898

prune219.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	449	0	449
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	449	8	457

Error

Counts

457 → 8

Alt Table

Status	Error	Program
▶	11.9b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
✓	11.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.7b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	13.7b	(*.f64 (/.f64 (/.f64 a1 1) 1) (/.f64 (/.f64 a2 b1) b2))
	28.0b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) (sqrt.f64 b2)) (sqrt.f64 b2))
	12.5b	(/.f64 (/.f64 a1 (*.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 b2 (/.f64 a2 (cbrt.f64 b1))))
	13.4b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 8470 to 1833 computations (78.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 b1) b2)
✓	11.5b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))

series40.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
11.0ms	(/.f64 (/.f64 1 b1) b2)

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`times-frac_binary64`
106×	`add-exp-log_binary64`
93×	`add-sqr-sqrt_binary64`
82×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`

Counts

2 → 176

Calls

2 calls:

17.0ms	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
4.0ms	(/.f64 (/.f64 1 b1) b2)

simplify149.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

413×	`unswap-sqr_binary64`
407×	`associate-/r/_binary64`
404×	`*-commutative_binary64`
368×	`associate-/r*_binary64`
319×	`sqr-pow_binary64`

Counts

248 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	3471
1	399	3103
2	1588	3091
3	2613	3091
4	3184	3091
5	3960	3091
6	5072	3091

prune145.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	247	8	255

Error

Counts

255 → 8

Alt Table

Status	Error	Program
✓	11.9b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
✓	11.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.7b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	13.7b	(*.f64 (/.f64 (/.f64 a1 1) 1) (/.f64 (/.f64 a2 b1) b2))
	28.0b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) (sqrt.f64 b2)) (sqrt.f64 b2))
	12.5b	(/.f64 (/.f64 a1 (*.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 b2 (/.f64 a2 (cbrt.f64 b1))))
	13.4b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 4898 to 2534 computations (48.3% saved)

regimes2.2s (39.2%)

Accuracy

Total 2.5b remaining (98.9%)

Threshold costs 0b (0%)

Counts

90 → 5

Compiler

Compiled 10694 to 6506 computations (39.2% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	113
1	36	113
2	35	113

end35.0ms (0.6%)

Compiler: Compiled 405 to 145 computations (64.2% saved)

sample1.2s (22.1%)

Algorithm

1×

intervals

Results

307.0ms	8000×	body	128	valid
65.0ms	1842×	body	128	invalid

Compiler

Compiled 204 to 110 computations (46.1% saved)

Details

analyze683.0ms (12.3%)

sample54.0ms (1%)

simplify8.0ms (0.1%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series35.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify85.0ms (1.5%)

prune32.0ms (0.6%)

localize5.0ms (0.1%)

series41.0ms (0.7%)

rewrite13.0ms (0.2%)

simplify96.0ms (1.7%)

prune75.0ms (1.3%)

localize5.0ms (0.1%)

series40.0ms (0.7%)

rewrite48.0ms (0.9%)

simplify284.0ms (5.1%)

prune219.0ms (3.9%)

localize7.0ms (0.1%)

series40.0ms (0.7%)

rewrite42.0ms (0.7%)

simplify149.0ms (2.7%)

prune145.0ms (2.6%)

regimes2.2s (39.2%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end35.0ms (0.6%)

sample1.2s (22.1%)

Profiling