Details

analyze850.0ms (22.3%)

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 (30.9%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

922.0ms	8256×	body	128	valid
214.0ms	1970×	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

11.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.4b	(/.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
✓	11.0b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series29.0ms (0.8%)

Counts

1 → 48

Calls

1 calls:

29.0ms

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

rewrite11.0ms (0.3%)

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 (2.2%)

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

prune29.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	7	37

Error

0.0b

Counts

37 → 7

Alt Table

Status	Error	Program
✓	11.4b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
▶	11.5b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.6b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	33.6b	(cbrt.f64 (pow.f64 (/.f64 (.f64 a1 a2) (.f64 b2 b1)) 3))
	12.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	12.0b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

Compiler

Compiled 603 to 212 computations (64.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (*.f64 b1 b2))
✓	11.0b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))

series40.0ms (1%)

Counts

2 → 72

Calls

2 calls:

32.0ms	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
8.0ms	(/.f64 1 (*.f64 b1 b2))

rewrite16.0ms (0.4%)

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))

simplify86.0ms (2.3%)

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

prune50.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	95	6	101

Error

0.0b

Counts

101 → 6

Alt Table

Status	Error	Program
	12.6b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	12.0b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
▶	11.4b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
✓	11.4b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 1466 to 629 computations (57.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(/.f64 1 (*.f64 b1 b2))
✓	5.6b	(.f64 a2 (/.f64 1 (.f64 b1 b2)))
✓	6.7b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))

series46.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

29.0ms	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
17.0ms	(.f64 a2 (/.f64 1 (.f64 b1 b2)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64`
28×	`prod-exp_binary64`
25×	`add-cbrt-cube_binary64`
12×	`cbrt-unprod_binary64`
9×	`pow1_binary64`

Counts

2 → 64

Calls

2 calls:

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

simplify119.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

516×	`associate-*r/_binary64`
515×	`times-frac_binary64`
437×	`associate-*l/_binary64`
306×	`sqr-pow_binary64`
227×	`fma-neg_binary64`

Counts

148 → 89

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	99	1536
1	218	1365
2	743	1365
3	3218	1365
4	3600	1365
5	4293	1365
6	4851	1365
7	4969	1365
8	5094	1365

prune71.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	127	7	134

Error

0.0b

Counts

134 → 7

Alt Table

Status	Error	Program
▶	10.6b	(.f64 a1 (.f64 (/.f64 a2 b1) (/.f64 1 b2)))
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	12.6b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	11.4b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
✓	11.4b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 1933 to 907 computations (53.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.5b	(*.f64 (/.f64 a2 b1) (/.f64 1 b2))
✓	6.7b	(.f64 a1 (.f64 (/.f64 a2 b1) (/.f64 1 b2)))

series44.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

27.0ms	(.f64 a1 (.f64 (/.f64 a2 b1) (/.f64 1 b2)))
17.0ms	(*.f64 (/.f64 a2 b1) (/.f64 1 b2))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64`
34×	`add-sqr-sqrt_binary64`
32×	`add-cbrt-cube_binary64`
25×	`times-frac_binary64`
25×	`prod-exp_binary64`

Counts

2 → 93

Calls

2 calls:

11.0ms	(*.f64 (/.f64 a2 b1) (/.f64 1 b2))
7.0ms	(.f64 a1 (.f64 (/.f64 a2 b1) (/.f64 1 b2)))

simplify121.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

573×	`associate-*l/_binary64`
338×	`associate-/l*_binary64`
329×	`fma-def_binary64`
315×	`unswap-sqr_binary64`
288×	`sqr-pow_binary64`

Counts

177 → 136

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	137	1987
1	328	1735
2	956	1735
3	2570	1735
4	3064	1735
5	3846	1735
6	4759	1735
7	4976	1735

prune75.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	136	7	143

Error

0.0b

Counts

143 → 7

Alt Table

Status	Error	Program
✓	10.6b	(.f64 a1 (.f64 (/.f64 a2 b1) (/.f64 1 b2)))
	12.2b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	11.9b	(*.f64 a1 (/.f64 (/.f64 a2 b2) b1))
	12.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	11.4b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
✓	11.4b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 2145 to 899 computations (58.1% saved)

regimes517.0ms (13.5%)

Accuracy

Total 3.1b remaining (98.9%)

Threshold costs 0b (0%)

Counts

27 → 5

Compiler

Compiled 3497 to 2039 computations (41.7% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	110
1	31	110
2	31	110

end370.0ms (9.7%)

Compiler: Compiled 555 to 203 computations (63.4% saved)

Details

analyze850.0ms (22.3%)

sample1.2s (30.9%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series29.0ms (0.8%)

rewrite11.0ms (0.3%)

simplify85.0ms (2.2%)

prune29.0ms (0.7%)

localize7.0ms (0.2%)

series40.0ms (1%)

rewrite16.0ms (0.4%)

simplify86.0ms (2.3%)

prune50.0ms (1.3%)

localize7.0ms (0.2%)

series46.0ms (1.2%)

rewrite18.0ms (0.5%)

simplify119.0ms (3.1%)

prune71.0ms (1.9%)

localize6.0ms (0.2%)

series44.0ms (1.1%)

rewrite25.0ms (0.7%)

simplify121.0ms (3.2%)

prune75.0ms (2%)

regimes517.0ms (13.5%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end370.0ms (9.7%)

Profiling