Details

analyze821.0ms (13.2%)

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)

sample1.1s (18.4%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

883.0ms	8256×	body	128	valid
221.0ms	1963×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% 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

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

10.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.6b	(/.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
✓	10.3b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series31.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

31.0ms

(/.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))

simplify84.0ms (1.4%)

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

prune39.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	28	8	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	9	37

Error

0.0b

Counts

37 → 9

Alt Table

Status	Error	Program
✓	10.6b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	11.2b	(.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))))
	10.9b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	10.9b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	8.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	9.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
▶	8.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	10.7b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

Compiler

Compiled 683 to 244 computations (64.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.3b	(/.f64 b1 (/.f64 a2 b2))
✓	6.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

series39.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

28.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
12.0ms	(/.f64 b1 (/.f64 a2 b2))

rewrite47.0ms (0.8%)

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:

11.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
4.0ms	(/.f64 b1 (/.f64 a2 b2))

simplify279.0ms (4.5%)

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

prune287.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	445	4	449
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	450	8	458

Error

Counts

458 → 8

Alt Table

Status	Error	Program
✓	8.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	8.4b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
	10.9b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
▶	8.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	11.6b	(/.f64 a1 (*.f64 (/.f64 b1 a2) b2))
	8.4b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	11.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

Compiler

Compiled 8440 to 1815 computations (78.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series27.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

27.0ms

(*.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:

9.0ms

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

simplify122.0ms (2%)

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

prune46.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	81	8	89

Error

Counts

89 → 8

Alt Table

Status	Error	Program
✓	8.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
▶	8.4b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
	10.9b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
✓	8.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	11.6b	(/.f64 a1 (*.f64 (/.f64 b1 a2) b2))
	8.4b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	11.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

Compiler

Compiled 1320 to 375 computations (71.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 1 (/.f64 b1 (/.f64 a2 b2)))
	2.3b	(/.f64 b1 (/.f64 a2 b2))
✓	6.8b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))

series43.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

27.0ms	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
16.0ms	(/.f64 1 (/.f64 b1 (/.f64 a2 b2)))

rewrite90.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

738×	`times-frac_binary64`
361×	`add-sqr-sqrt_binary64`
341×	`*-un-lft-identity_binary64`
338×	`add-cube-cbrt_binary64`
137×	`associate-r_binary64`

Counts

2 → 380

Calls

2 calls:

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

simplify366.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
487×	`fma-neg_binary64`
318×	`associate-/r/_binary64`
224×	`sqr-pow_binary64`
209×	`*-commutative_binary64`

Counts

464 → 599

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	7873
1	673	7145
2	2365	7019
3	2498	7019
4	3198	7019
5	3597	7019
6	4429	7019
7	4998	7019
8	4972	7019

prune408.0ms (6.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	713	0	713
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	713	8	721

Error

Counts

721 → 8

Alt Table

Status	Error	Program
✓	8.2b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	8.4b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
	10.9b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
✓	8.3b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	10.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	11.6b	(/.f64 a1 (*.f64 (/.f64 b1 a2) b2))
	8.4b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
	11.2b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

Compiler

Compiled 14669 to 5001 computations (65.9% saved)

regimes1.9s (30.7%)

Accuracy

Total 2.6b remaining (99.1%)

Threshold costs 0b (0%)

Counts

127 → 5

Compiler

Compiled 19298 to 10963 computations (43.2% saved)

bsearch4.0ms (0.1%)

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	39	143
1	44	143
2	43	143

end379.0ms (6.1%)

Compiler: Compiled 686 to 270 computations (60.6% saved)

Details

analyze821.0ms (13.2%)

sample1.1s (18.4%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series31.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify84.0ms (1.4%)

prune39.0ms (0.6%)

localize5.0ms (0.1%)

series39.0ms (0.6%)

rewrite47.0ms (0.8%)

simplify279.0ms (4.5%)

prune287.0ms (4.6%)

localize5.0ms (0.1%)

series27.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify122.0ms (2%)

prune46.0ms (0.7%)

localize6.0ms (0.1%)

series43.0ms (0.7%)

rewrite90.0ms (1.4%)

simplify366.0ms (5.9%)

prune408.0ms (6.6%)

regimes1.9s (30.7%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end379.0ms (6.1%)

Profiling