Details

analyze736.0ms (10.5%)

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)

sample48.0ms (0.7%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

9.0ms	256×	body	128	valid
3.0ms	49×	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

prune4.0ms (0.1%)

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
✓	11.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series35.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

35.0ms

(/.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))

simplify93.0ms (1.3%)

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

prune32.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	28	8	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	8	37

Error

0.0b

Counts

37 → 8

Alt Table

Status	Error	Program
	9.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	9.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	12.1b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.1b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
▶	9.1b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	30.2b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 654 to 235 computations (64.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

series35.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

35.0ms

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

rewrite12.0ms (0.2%)

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:

8.0ms

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

simplify125.0ms (1.8%)

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

prune52.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Error

0.0b

Counts

89 → 9

Alt Table

Status	Error	Program
	20.4b	(*.f64 (/.f64 (/.f64 a1 b1) (sqrt.f64 b2)) (/.f64 a2 (sqrt.f64 b2)))
	9.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	9.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	12.1b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.1b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	10.2b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)
	30.2b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))

Compiler

Compiled 1392 to 411 computations (70.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.3b	(/.f64 (*.f64 a1 a2) b1)
✓	5.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

series42.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.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)

simplify94.0ms (1.3%)

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

prune76.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Error

Counts

109 → 8

Alt Table

Status	Error	Program
	21.6b	(.f64 (/.f64 (.f64 a1 a2) (sqrt.f64 b2)) (/.f64 (/.f64 1 b1) (sqrt.f64 b2)))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
▶	6.8b	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2)))
	9.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.1b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.1b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	10.2b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)

Compiler

Compiled 1574 to 461 computations (70.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 b1)
✓	1.8b	(/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2))
✓	3.1b	(/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (.f64 (cbrt.f64 b2) (cbrt.f64 b2)))
✓	3.3b	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2)))

series2.6s (36.5%)

Counts

4 → 132

Calls

4 calls:

1.6s	(/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (.f64 (cbrt.f64 b2) (cbrt.f64 b2)))
835.0ms	(/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2))
62.0ms	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2)))
32.0ms	(cbrt.f64 b1)

rewrite153.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

572×	`times-frac_binary64`
344×	`add-sqr-sqrt_binary64`
272×	`*-un-lft-identity_binary64`
272×	`add-cube-cbrt_binary64`
270×	`cbrt-prod_binary64`

Counts

4 → 454

Calls

4 calls:

44.0ms	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2)))
8.0ms	(/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (.f64 (cbrt.f64 b2) (cbrt.f64 b2)))
7.0ms	(/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2))
1.0ms	(cbrt.f64 b1)

simplify346.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

475×	`associate-/l*_binary64`
456×	`associate-/l/_binary64`
407×	`associate-/r*_binary64`
330×	`associate-l_binary64`
302×	`times-frac_binary64`

Counts

586 → 693

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	590	18570
1	1627	14752
2	4857	14712
3	5035	14712

prune333.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	727	0	727
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	727	8	735

Error

Counts

735 → 8

Alt Table

Status	Error	Program
	21.6b	(.f64 (/.f64 (.f64 a1 a2) (sqrt.f64 b2)) (/.f64 (/.f64 1 b1) (sqrt.f64 b2)))
	12.3b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
✓	6.8b	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2)))
	9.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.1b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.1b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	10.2b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)

Compiler

Compiled 23849 to 3858 computations (83.8% saved)

regimes1.1s (15.8%)

Accuracy

Total 3.7b remaining (99.1%)

Threshold costs 0b (0%)

Counts

75 → 5

Compiler

Compiled 9114 to 5577 computations (38.8% 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×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	137
1	42	137
2	41	137

end33.0ms (0.5%)

Compiler: Compiled 475 to 160 computations (66.3% saved)

sample1.0s (14.8%)

Algorithm

1×

intervals

Results

273.0ms	8000×	body	128	valid
60.0ms	1748×	body	128	invalid

Compiler

Compiled 223 to 114 computations (48.9% saved)

Details

analyze736.0ms (10.5%)

sample48.0ms (0.7%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series35.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify93.0ms (1.3%)

prune32.0ms (0.5%)

localize5.0ms (0.1%)

series35.0ms (0.5%)

rewrite12.0ms (0.2%)

simplify125.0ms (1.8%)

prune52.0ms (0.7%)

localize8.0ms (0.1%)

series42.0ms (0.6%)

rewrite13.0ms (0.2%)

simplify94.0ms (1.3%)

prune76.0ms (1.1%)

localize14.0ms (0.2%)

series2.6s (36.5%)

rewrite153.0ms (2.2%)

simplify346.0ms (4.9%)

prune333.0ms (4.7%)

regimes1.1s (15.8%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end33.0ms (0.5%)

sample1.0s (14.8%)

Profiling