Details

analyze845.0ms (19.3%)

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)

sample1.2s (27.9%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

947.0ms	8256×	body	128	valid
231.0ms	1998×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% 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

10.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.5b	(/.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
✓	10.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series29.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

29.0ms

(/.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))

simplify90.0ms (2.1%)

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

prune30.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	8	37

Error

0.0b

Counts

37 → 8

Alt Table

Status	Error	Program
	11.4b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
▶	10.6b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.9b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	29.2b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (sqrt.f64 (/.f64 (.f64 a1 a2) (*.f64 b1 b2))))
	33.0b	(cbrt.f64 (pow.f64 (/.f64 (.f64 a1 a2) (.f64 b2 b1)) 3))
	13.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

Compiler

Compiled 645 to 230 computations (64.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (*.f64 b1 b2))
✓	10.1b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))

series36.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

27.0ms	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
9.0ms	(/.f64 1 (*.f64 b1 b2))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
30×	`prod-exp_binary64`
28×	`add-cbrt-cube_binary64`
12×	`cbrt-unprod_binary64`
12×	`div-exp_binary64`

Counts

2 → 72

Calls

2 calls:

7.0ms	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
3.0ms	(/.f64 1 (*.f64 b1 b2))

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-*r/_binary64`
437×	`associate-*l/_binary64`
362×	`unswap-sqr_binary64`
313×	`associate-/l*_binary64`
310×	`sqr-pow_binary64`

Counts

144 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	91	1533
1	210	1338
2	760	1338
3	2722	1338
4	3207	1338
5	4011	1338
6	5038	1338

prune69.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	95	7	102

Error

0.0b

Counts

102 → 7

Alt Table

Status	Error	Program
	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
▶	10.4b	(.f64 (.f64 a1 a2) (/.f64 (/.f64 1 b1) b2))
	13.3b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))
	12.9b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	13.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 1492 to 647 computations (56.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 b1) b2)
✓	10.1b	(.f64 (.f64 a1 a2) (/.f64 (/.f64 1 b1) b2))

series37.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(.f64 (.f64 a1 a2) (/.f64 (/.f64 1 b1) b2))
8.0ms	(/.f64 (/.f64 1 b1) b2)

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
79×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64`
46×	`add-exp-log_binary64`

Counts

2 → 147

Calls

2 calls:

13.0ms	(.f64 (.f64 a1 a2) (/.f64 (/.f64 1 b1) b2))
5.0ms	(/.f64 (/.f64 1 b1) b2)

simplify144.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

876×	`times-frac_binary64`
588×	`associate-/l*_binary64`
523×	`associate-*l/_binary64`
268×	`associate-/r*_binary64`
259×	`associate-/l/_binary64`

Counts

219 → 204

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	146	2966
1	377	2673
2	1311	2673
3	4354	2673
4	4514	2673
5	4989	2673
6	4979	2673

prune118.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	203	8	211

Error

Counts

211 → 8

Alt Table

Status	Error	Program
▶	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	10.4b	(.f64 (.f64 a1 a2) (/.f64 (/.f64 1 b1) b2))
	11.4b	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b1) b2)))
	12.9b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	23.9b	(.f64 (/.f64 (.f64 a1 a2) (sqrt.f64 b2)) (/.f64 (/.f64 1 b1) (sqrt.f64 b2)))
	13.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 3781 to 1803 computations (52.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.7b	(/.f64 b1 (/.f64 a2 b2))
✓	5.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

series42.0ms (1%)

Counts

2 → 84

Calls

2 calls:

28.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
13.0ms	(/.f64 b1 (/.f64 a2 b2))

rewrite46.0ms (1%)

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:

9.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
4.0ms	(/.f64 b1 (/.f64 a2 b2))

simplify271.0ms (6.2%)

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

prune192.0ms (4.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	450	7	457

Error

Counts

457 → 7

Alt Table

Status	Error	Program
✓	11.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	10.4b	(.f64 (.f64 a1 a2) (/.f64 (/.f64 1 b1) b2))
	12.9b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	9.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	13.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 8346 to 1753 computations (79% saved)

regimes747.0ms (17%)

Accuracy

Total 2.5b remaining (99.2%)

Threshold costs 0b (0%)

Counts

39 → 5

Compiler

Compiled 5119 to 3171 computations (38.1% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	113
1	38	113
2	37	113

end279.0ms (6.4%)

Remove: (sort a1 a2)
Compiler: Compiled 727 to 283 computations (61.1% saved)

Details

analyze845.0ms (19.3%)

sample1.2s (27.9%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series29.0ms (0.7%)

rewrite6.0ms (0.1%)

simplify90.0ms (2.1%)

prune30.0ms (0.7%)

localize6.0ms (0.1%)

series36.0ms (0.8%)

rewrite15.0ms (0.3%)

simplify91.0ms (2.1%)

prune69.0ms (1.6%)

localize7.0ms (0.1%)

series37.0ms (0.8%)

rewrite34.0ms (0.8%)

simplify144.0ms (3.3%)

prune118.0ms (2.7%)

localize5.0ms (0.1%)

series42.0ms (1%)

rewrite46.0ms (1%)

simplify271.0ms (6.2%)

prune192.0ms (4.4%)

regimes747.0ms (17%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end279.0ms (6.4%)

Profiling