Details

analyze1.0s (20.3%)

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)

sample38.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
2.0ms	60×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify10.0ms (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

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

11.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.8b	(/.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
✓	11.4b	(/.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))

series102.0ms (2%)

Counts

1 → 48

Calls

1 calls:

102.0ms

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

simplify100.0ms (2%)

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 → 91

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

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	8	92

Error

0.0b

Counts

92 → 8

Alt Table

Status	Error	Program
	12.3b	(.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))))
✓	11.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	10.1b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	14.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	14.9b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	27.7b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 673 to 226 computations (66.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.4b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	5.5b	(/.f64 (*.f64 a1 a2) b1)

rewrite16.0ms (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 (/.f64 (*.f64 a1 a2) b1) b2)
3.0ms	(/.f64 (*.f64 a1 a2) b1)

series148.0ms (3%)

Counts

2 → 48

Calls

2 calls:

98.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
50.0ms	(/.f64 (*.f64 a1 a2) b1)

simplify117.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

820×	`associate-/l*_binary64`
608×	`associate-/l/_binary64`
389×	`associate-*l/_binary64`
362×	`associate-/r*_binary64`
287×	`associate-l_binary64`

Counts

121 → 162

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

prune80.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	161	9	170

Error

Counts

170 → 9

Alt Table

Status	Error	Program
✓	11.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	20.0b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) (sqrt.f64 b2)) (sqrt.f64 b2))
	38.3b	(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) b1)) (sqrt.f64 b2)) (/.f64 (sqrt.f64 (/.f64 (*.f64 a1 a2) b1)) (sqrt.f64 b2)))
	11.7b	(/.f64 (/.f64 a1 1) (*.f64 b2 (/.f64 b1 a2)))
▶	10.1b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))
	10.4b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	12.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	20.2b	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (sqrt.f64 b2)) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (sqrt.f64 b2)))

Compiler

Compiled 1614 to 478 computations (70.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.4b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))
	5.5b	(/.f64 (*.f64 a1 a2) b1)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`prod-exp_binary64`
14×	`times-frac_binary64`

Counts

1 → 56

Calls

1 calls:

10.0ms

(*.f64 (/.f64 (*.f64 a1 a2) b1) (/.f64 1 b2))

series100.0ms (2%)

Counts

1 → 48

Calls

1 calls:

100.0ms

(*.f64 (/.f64 (*.f64 a1 a2) b1) (/.f64 1 b2))

simplify124.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

687×	`times-frac_binary64`
668×	`associate-/l*_binary64`
255×	`fma-neg_binary64`
241×	`sqr-pow_binary64`
238×	`unswap-sqr_binary64`

Counts

104 → 153

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	104	1350
1	257	1173
2	892	1173
3	3059	1173
4	3544	1173
5	4192	1173
6	4891	1173
7	4969	1173

prune74.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	185	9	194

Error

Counts

194 → 9

Alt Table

Status	Error	Program
	11.9b	(.f64 (.f64 a1 a2) (*.f64 (/.f64 1 b1) (/.f64 1 b2)))
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	11.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	20.0b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) (sqrt.f64 b2)) (sqrt.f64 b2))
	11.7b	(/.f64 (/.f64 a1 1) (*.f64 b2 (/.f64 b1 a2)))
✓	10.1b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))
▶	10.4b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	12.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	20.2b	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (sqrt.f64 b2)) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (sqrt.f64 b2)))

Compiler

Compiled 1834 to 733 computations (60% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.4b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
✓	5.7b	(*.f64 a1 (/.f64 a2 b1))

rewrite14.0ms (0.3%)

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:

7.0ms	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
5.0ms	(*.f64 a1 (/.f64 a2 b1))

series145.0ms (2.9%)

Counts

2 → 84

Calls

2 calls:

99.0ms	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
46.0ms	(*.f64 a1 (/.f64 a2 b1))

simplify128.0ms (2.6%)

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 → 233

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

prune49.0ms (1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	233	9	242

Error

Counts

242 → 9

Alt Table

Status	Error	Program
	11.7b	(/.f64 (/.f64 a1 1) (*.f64 b2 (/.f64 b1 a2)))
	10.9b	(/.f64 1 (/.f64 b2 (*.f64 a1 (/.f64 a2 b1))))
	11.9b	(.f64 (.f64 a1 a2) (*.f64 (/.f64 1 b1) (/.f64 1 b2)))
	11.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	11.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
✓	10.1b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))
✓	10.4b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	12.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	20.2b	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (sqrt.f64 b2)) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (sqrt.f64 b2)))

Compiler

Compiled 1227 to 378 computations (69.2% saved)

regimes1.5s (30.1%)

Accuracy

Total 3.0b remaining (96.7%)

Threshold costs 0b (0%)

Compiler

Compiled 9467 to 5427 computations (42.7% saved)

bsearch3.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	149
1	40	149
2	39	149

end32.0ms (0.6%)

Remove: (sort a1 a2)
Compiler: Compiled 714 to 217 computations (69.6% saved)

sample1.1s (22.4%)

Algorithm

1×

intervals

Results

312.0ms	8000×	body	128	valid
63.0ms	1832×	body	128	invalid

Compiler

Compiled 240 to 123 computations (48.8% saved)

Details

analyze1.0s (20.3%)

sample38.0ms (0.8%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite5.0ms (0.1%)

series102.0ms (2%)

simplify100.0ms (2%)

prune29.0ms (0.6%)

localize5.0ms (0.1%)

rewrite16.0ms (0.3%)

series148.0ms (3%)

simplify117.0ms (2.4%)

prune80.0ms (1.6%)

localize6.0ms (0.1%)

rewrite13.0ms (0.3%)

series100.0ms (2%)

simplify124.0ms (2.5%)

prune74.0ms (1.5%)

localize5.0ms (0.1%)

rewrite14.0ms (0.3%)

series145.0ms (2.9%)

simplify128.0ms (2.6%)

prune49.0ms (1%)

regimes1.5s (30.1%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end32.0ms (0.6%)

sample1.1s (22.4%)

Profiling