Details

analyze1.2s (12%)

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)

sample86.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
2.0ms	61×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (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 → 0

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

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

12.2b

Counts

1 → 1

Alt Table

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

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

11.8b

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

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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 → 21

Calls

1 calls:

4.0ms

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

Compiler

Compiled 295 to 77 computations (73.9% saved)

series29.0ms (0.3%)

Error

12.2b

Counts

1 → 12

Calls

1 calls:

29.0ms

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

Compiler

Compiled 275 to 175 computations (36.4% saved)

simplify90.0ms (0.9%)

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

33 → 18

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	475
1	159	370
2	818	370
3	3796	370
4	4099	370
5	4405	370
6	4893	370
7	5221	370

prune16.0ms (0.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	12	6	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	6	19

Error

0.1b

Counts

19 → 6

Alt Table

Status	Error	Program
	11.2b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.2b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	12.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b2 b1))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b2 b1)))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b2 b1))))
▶	10.1b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.3b	(/.f64 1 (/.f64 (.f64 b2 b1) (.f64 a1 a2)))
	28.5b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b2 b1))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b2 b1))))

Compiler

Compiled 314 to 136 computations (56.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

5.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
5.9b	(/.f64 b1 (/.f64 a2 b2))

rewrite242.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

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 → 266

Calls

2 calls:

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

Compiler

Compiled 5189 to 1256 computations (75.8% saved)

series45.0ms (0.4%)

Error

0.0b

Counts

2 → 21

Calls

2 calls:

27.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
16.0ms	(/.f64 b1 (/.f64 a2 b2))

Compiler

Compiled 480 to 303 computations (36.9% saved)

simplify368.0ms (3.6%)

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

287 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	6523
1	990	6310
2	3654	6307
3	3575	6307
4	4143	6307
5	4464	6307
6	4953	6307
7	4964	6307

prune131.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	217	8	225

Error

Counts

225 → 8

Alt Table

Status	Error	Program
	11.2b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.2b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	23.6b	(*.f64 (/.f64 1 (sqrt.f64 b2)) (/.f64 a1 (/.f64 b1 (/.f64 a2 (sqrt.f64 b2)))))
	9.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
▶	4.4b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
	12.0b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	10.9b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) b1) (*.f64 (/.f64 a2 b2) (cbrt.f64 a1)))
	13.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))

Compiler

Compiled 3244 to 715 computations (78% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))
1.2b	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))))
1.7b	(/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))

rewrite2.7s (26.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

5182×	`times-frac_binary64`
2568×	`cbrt-prod_binary64`
2472×	`add-sqr-sqrt_binary64`
2295×	`*-un-lft-identity_binary64`
2295×	`add-cube-cbrt_binary64`

Counts

4 → 2181

Calls

4 calls:

226.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
90.0ms	(/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
11.0ms	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))))
9.0ms	(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))

Compiler

Compiled 100870 to 12220 computations (87.9% saved)

series308.0ms (3%)

Error

Counts

4 → 42

Calls

4 calls:

91.0ms	(/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
85.0ms	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))))
56.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
55.0ms	(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))

Compiler

Compiled 3285 to 1992 computations (39.4% saved)

simplify1.7s (16.5%)

Algorithm

1×	egg-herbie

Rules

914×	`associate-/r/_binary64`
557×	`associate-*l/_binary64`
555×	`associate-*r/_binary64`
143×	`associate-/l*_binary64`
37×	`associate-/r*_binary64`

Counts

2223 → 1715

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1926	99753
1	4970	99753
2	4999	99753

prune567.0ms (5.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1715	0	1715
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	1715	8	1723

Error

Counts

1723 → 8

Alt Table

Status	Error	Program
	11.2b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.2b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	23.6b	(*.f64 (/.f64 1 (sqrt.f64 b2)) (/.f64 a1 (/.f64 b1 (/.f64 a2 (sqrt.f64 b2)))))
▶	9.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
✓	4.4b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
	12.0b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	10.9b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) b1) (*.f64 (/.f64 a2 b2) (cbrt.f64 a1)))
	13.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))

Compiler

Compiled 38737 to 3368 computations (91.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

4.2b	(/.f64 a2 (*.f64 b2 b1))
5.6b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

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 → 48

Calls

2 calls:

6.0ms	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
3.0ms	(/.f64 a2 (*.f64 b2 b1))

Compiler

Compiled 606 to 154 computations (74.6% saved)

series44.0ms (0.4%)

Error

Counts

2 → 21

Calls

2 calls:

27.0ms	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
16.0ms	(/.f64 a2 (*.f64 b2 b1))

Compiler

Compiled 480 to 303 computations (36.9% saved)

simplify116.0ms (1.1%)

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

69 → 26

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	831
1	190	702
2	734	702
3	3955	702
4	4324	702
5	4873	702
6	4889	702
7	5147	702

prune16.0ms (0.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	26	8	34

Error

Counts

34 → 8

Alt Table

Status	Error	Program
	11.2b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.2b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b2 b1)))
	10.8b	(*.f64 a1 (/.f64 1 (/.f64 b2 (/.f64 a2 b1))))
	9.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	4.4b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
	12.0b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	10.9b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) b1) (*.f64 (/.f64 a2 b2) (cbrt.f64 a1)))
	13.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))

Compiler

Compiled 305 to 129 computations (57.7% saved)

regimes1.2s (12.1%)

Accuracy

Total 3.1b remaining (99.1%)

Threshold costs 0b (0%)

Compiler

Compiled 21724 to 12357 computations (43.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	58
1	21	58
2	21	58

end48.0ms (0.5%)

Remove: (sort b1 b2)
Compiler: Compiled 273 to 133 computations (51.3% saved)

sample1.1s (11.2%)

Algorithm

1×

intervals

Results

307.0ms	8000×	body	128	valid
66.0ms	1794×	body	128	invalid

Compiler

Compiled 175 to 103 computations (41.1% saved)

Details

analyze1.2s (12%)

sample86.0ms (0.8%)

simplify14.0ms (0.1%)

prune1.0ms (0%)

localize6.0ms (0.1%)

rewrite23.0ms (0.2%)

series29.0ms (0.3%)

simplify90.0ms (0.9%)

prune16.0ms (0.2%)

localize6.0ms (0.1%)

rewrite242.0ms (2.4%)

series45.0ms (0.4%)

simplify368.0ms (3.6%)

prune131.0ms (1.3%)

localize22.0ms (0.2%)

rewrite2.7s (26.3%)

series308.0ms (3%)

simplify1.7s (16.5%)

prune567.0ms (5.6%)

localize7.0ms (0.1%)

rewrite40.0ms (0.4%)

series44.0ms (0.4%)

simplify116.0ms (1.1%)

prune16.0ms (0.2%)

regimes1.2s (12.1%)

simplify5.0ms (0.1%)

end48.0ms (0.5%)

sample1.1s (11.2%)

Profiling