Details

analyze846.0ms (20.4%)

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 (27.5%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

888.0ms	8256×	body	128	valid
202.0ms	1832×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify8.0ms (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))

series30.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

30.0ms

(/.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))

simplify84.0ms (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 → 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
	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	11.8b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	10.7b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
▶	10.6b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	14.0b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

Compiler

Compiled 623 to 224 computations (64% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
✓	9.9b	(/.f64 (.f64 b1 b2) (.f64 a1 a2))

series62.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

31.0ms	(/.f64 (.f64 b1 b2) (.f64 a1 a2))
30.0ms	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
26×	`div-exp_binary64`
20×	`times-frac_binary64`
16×	`prod-exp_binary64`

Counts

2 → 81

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
4.0ms	(/.f64 (.f64 b1 b2) (.f64 a1 a2))

simplify94.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-*l/_binary64`
648×	`associate-l_binary64`
526×	`associate-*r/_binary64`
496×	`associate-/l/_binary64`
461×	`associate-/r/_binary64`

Counts

177 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	2403
1	226	2062
2	1133	2041
3	4579	2041
4	4937	2041
5	5030	2041

prune76.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	111	10	121

Error

0.0b

Counts

121 → 10

Alt Table

Status	Error	Program
	11.8b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	14.8b	(*.f64 (/.f64 1 (/.f64 b1 a1)) (/.f64 1 (/.f64 b2 a2)))
	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	10.7b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
✓	10.6b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
▶	9.8b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a1) a2))
	12.2b	(/.f64 1 (/.f64 b1 (/.f64 (*.f64 a1 a2) b2)))
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

Compiler

Compiled 1963 to 687 computations (65% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a1) a2))
✓	5.0b	(/.f64 (/.f64 (*.f64 b1 b2) a1) a2)
✓	6.4b	(/.f64 (*.f64 b1 b2) a1)

series72.0ms (1.7%)

Counts

3 → 132

Calls

3 calls:

30.0ms	(/.f64 (/.f64 (*.f64 b1 b2) a1) a2)
28.0ms	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a1) a2))
13.0ms	(/.f64 (*.f64 b1 b2) a1)

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

231×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
103×	`add-cube-cbrt_binary64`
51×	`add-exp-log_binary64`

Counts

3 → 207

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a1) a2))
5.0ms	(/.f64 (/.f64 (*.f64 b1 b2) a1) a2)
3.0ms	(/.f64 (*.f64 b1 b2) a1)

simplify218.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

977×	`fma-neg_binary64`
407×	`fma-def_binary64`
377×	`*-commutative_binary64`
306×	`sqr-pow_binary64`
248×	`unswap-sqr_binary64`

Counts

339 → 311

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	5323
1	445	4751
2	1489	4706
3	2162	4706
4	2895	4706
5	3635	4706
6	4728	4706
7	5242	4706

prune184.0ms (4.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	307	4	311
Fresh	3	4	7
Picked	1	0	1
Done	1	1	2
Total	312	9	321

Error

Counts

321 → 9

Alt Table

Status	Error	Program
	14.8b	(*.f64 (/.f64 1 (/.f64 b1 a1)) (/.f64 1 (/.f64 b2 a2)))
▶	9.6b	(/.f64 a2 (/.f64 (*.f64 b2 b1) a1))
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	9.9b	(.f64 (/.f64 a1 (.f64 b2 b1)) a2)
	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.2b	(/.f64 1 (/.f64 b1 (/.f64 (*.f64 a1 a2) b2)))
	10.3b	(*.f64 (/.f64 1 b1) (/.f64 a2 (/.f64 b2 a1)))
	10.1b	(.f64 (/.f64 (.f64 (cbrt.f64 a2) (cbrt.f64 a2)) (/.f64 b1 (*.f64 (cbrt.f64 a1) (cbrt.f64 a1)))) (/.f64 (cbrt.f64 a2) (/.f64 b2 (cbrt.f64 a1))))
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 5717 to 1838 computations (67.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.1b	(/.f64 a2 (/.f64 (*.f64 b2 b1) a1))
✓	6.4b	(/.f64 (*.f64 b2 b1) a1)

series41.0ms (1%)

Counts

2 → 48

Calls

2 calls:

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

rewrite13.0ms (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 a2 (/.f64 (*.f64 b2 b1) a1))
3.0ms	(/.f64 (*.f64 b2 b1) a1)

simplify103.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

830×	`times-frac_binary64`
634×	`associate-/l*_binary64`
465×	`associate-/l/_binary64`
446×	`associate-/r/_binary64`
428×	`associate-/r*_binary64`

Counts

121 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1656
1	292	1524
2	1019	1518
3	4417	1518
4	4812	1518
5	4970	1518
6	4976	1518

prune58.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Error

Counts

112 → 9

Alt Table

Status	Error	Program
	14.8b	(*.f64 (/.f64 1 (/.f64 b1 a1)) (/.f64 1 (/.f64 b2 a2)))
✓	9.6b	(/.f64 a2 (/.f64 (*.f64 b2 b1) a1))
✓	10.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	9.9b	(.f64 (/.f64 a1 (.f64 b2 b1)) a2)
	11.8b	(/.f64 a2 (*.f64 b2 (/.f64 b1 a1)))
	10.3b	(*.f64 (/.f64 1 b1) (/.f64 a2 (/.f64 b2 a1)))
	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.2b	(/.f64 1 (/.f64 b1 (/.f64 (*.f64 a1 a2) b2)))
	12.5b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 1453 to 395 computations (72.8% saved)

regimes748.0ms (18%)

Accuracy

Total 2.1b remaining (99.5%)

Threshold costs 0b (0%)

Counts

40 → 5

Compiler

Compiled 4871 to 2971 computations (39% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	140
1	43	140
2	42	140

end256.0ms (6.2%)

Remove: (sort a1 a2)
Compiler: Compiled 883 to 367 computations (58.4% saved)

Details

analyze846.0ms (20.4%)

sample1.1s (27.5%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series30.0ms (0.7%)

rewrite6.0ms (0.1%)

simplify84.0ms (2%)

prune30.0ms (0.7%)

localize6.0ms (0.1%)

series62.0ms (1.5%)

rewrite16.0ms (0.4%)

simplify94.0ms (2.3%)

prune76.0ms (1.8%)

localize6.0ms (0.1%)

series72.0ms (1.7%)

rewrite38.0ms (0.9%)

simplify218.0ms (5.3%)

prune184.0ms (4.4%)

localize5.0ms (0.1%)

series41.0ms (1%)

rewrite13.0ms (0.3%)

simplify103.0ms (2.5%)

prune58.0ms (1.4%)

regimes748.0ms (18%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end256.0ms (6.2%)

Profiling