Details

analyze858.0ms (14.3%)

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 (20.5%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

964.0ms	8256×	body	128	valid
226.0ms	1881×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify9.0ms (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

prune1.0ms (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

9.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.5b	(/.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
✓	9.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series30.0ms (0.5%)

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))

simplify85.0ms (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

prune31.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	7	37

Error

0.0b

Counts

37 → 7

Alt Table

Status	Error	Program
	11.9b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.5b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	12.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
▶	8.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	10.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	40.0b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 a1 a2) (.f64 a1 a2)) (.f64 a1 a2)) (.f64 (.f64 (.f64 b1 b2) (.f64 b1 b2)) (.f64 b1 b2))))

Compiler

Compiled 642 to 223 computations (65.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.8b	(/.f64 (*.f64 b1 b2) a2)
✓	5.2b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

series49.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
13.0ms	(/.f64 (*.f64 b1 b2) a2)

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

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
673×	`associate-/l*_binary64`
506×	`associate-/l/_binary64`
500×	`associate-*l/_binary64`
480×	`associate-/r/_binary64`

Counts

157 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1914
1	291	1782
2	1078	1770
3	4951	1770
4	5016	1770

prune84.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	119	9	128

Error

Counts

128 → 9

Alt Table

Status	Error	Program
	8.4b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.5b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	8.2b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a2) a1))
✓	8.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
▶	8.2b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	12.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	9.3b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 b1 (*.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 b2 (cbrt.f64 a2))))
	8.8b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (.f64 (cbrt.f64 (/.f64 (.f64 b1 b2) a2)) (cbrt.f64 (/.f64 (.f64 b1 b2) a2)))) (/.f64 (cbrt.f64 a1) (cbrt.f64 (/.f64 (.f64 b1 b2) a2))))

Compiler

Compiled 1890 to 527 computations (72.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.5b	(/.f64 a1 (*.f64 b1 b2))
✓	4.7b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)

series51.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
19.0ms	(/.f64 a1 (*.f64 b1 b2))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-l_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

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

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

849×	`times-frac_binary64`
615×	`associate-*l/_binary64`
544×	`associate-l_binary64`
440×	`associate-/l*_binary64`
436×	`associate-*r/_binary64`

Counts

136 → 82

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	87	1426
1	202	1294
2	765	1294
3	4016	1294
4	4307	1294
5	4942	1294
6	4973	1294

prune58.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	82	9	91

Error

Counts

91 → 9

Alt Table

Status	Error	Program
	8.4b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.5b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
▶	8.2b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a2) a1))
✓	8.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
✓	8.2b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	12.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	9.3b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 b1 (*.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 b2 (cbrt.f64 a2))))
	8.8b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (.f64 (cbrt.f64 (/.f64 (.f64 b1 b2) a2)) (cbrt.f64 (/.f64 (.f64 b1 b2) a2)))) (/.f64 (cbrt.f64 a1) (cbrt.f64 (/.f64 (.f64 b1 b2) a2))))

Compiler

Compiled 1279 to 389 computations (69.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a2) a1))
	3.8b	(/.f64 (*.f64 b1 b2) a2)
✓	5.3b	(/.f64 (/.f64 (*.f64 b1 b2) a2) a1)

series64.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

33.0ms	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a2) a1))
31.0ms	(/.f64 (/.f64 (*.f64 b1 b2) a2) a1)

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`times-frac_binary64`
100×	`*-un-lft-identity_binary64`
100×	`add-sqr-sqrt_binary64`
100×	`add-cube-cbrt_binary64`
45×	`add-exp-log_binary64`

Counts

2 → 184

Calls

2 calls:

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

simplify198.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

666×	`associate-/r*_binary64`
565×	`associate-l_binary64`
517×	`associate-r_binary64`
298×	`*-commutative_binary64`
275×	`fma-def_binary64`

Counts

280 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	4825
1	421	4283
2	1430	4238
3	3913	4238
4	4571	4238
5	4969	4238
6	4978	4238

prune992.0ms (16.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	309	9	318

Error

Counts

318 → 9

Alt Table

Status	Error	Program
	8.4b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.5b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
✓	8.2b	(/.f64 1 (/.f64 (/.f64 (*.f64 b1 b2) a2) a1))
✓	8.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
✓	8.2b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	12.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	12.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	9.3b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 b1 (*.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 b2 (cbrt.f64 a2))))
	8.8b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (.f64 (cbrt.f64 (/.f64 (.f64 b1 b2) a2)) (cbrt.f64 (/.f64 (.f64 b1 b2) a2)))) (/.f64 (cbrt.f64 a1) (cbrt.f64 (/.f64 (.f64 b1 b2) a2))))

Compiler

Compiled 5607 to 1763 computations (68.6% saved)

regimes1.6s (26.1%)

Accuracy

Total 3.9b remaining (99.2%)

Threshold costs 0b (0%)

Counts

102 → 5

Compiler

Compiled 14351 to 8660 computations (39.7% saved)

bsearch3.0ms (0.1%)

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

simplify5.0ms (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	42	147
1	47	147
2	46	147

end427.0ms (7.1%)

Compiler: Compiled 743 to 305 computations (59% saved)

Details

analyze858.0ms (14.3%)

sample1.2s (20.5%)

simplify9.0ms (0.1%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series30.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify85.0ms (1.4%)

prune31.0ms (0.5%)

localize5.0ms (0.1%)

series49.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify82.0ms (1.4%)

prune84.0ms (1.4%)

localize5.0ms (0.1%)

series51.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify101.0ms (1.7%)

prune58.0ms (1%)

localize7.0ms (0.1%)

series64.0ms (1.1%)

rewrite34.0ms (0.6%)

simplify198.0ms (3.3%)

prune992.0ms (16.5%)

regimes1.6s (26.1%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end427.0ms (7.1%)

Profiling