Details

analyze861.0ms (16.6%)

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 (23.3%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

942.0ms	8256×	body	128	valid
221.0ms	1890×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify16.0ms (0.3%)

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

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
✓	10.4b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series28.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

28.0ms

(/.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:

5.0ms

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

simplify87.0ms (1.7%)

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

prune33.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	28	8	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	8	37

Error

0.0b

Counts

37 → 8

Alt Table

Status	Error	Program
▶	9.4b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	10.8b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	11.2b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	12.9b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	11.1b	(.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))))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	12.0b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	10.6b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

Compiler

Compiled 672 to 237 computations (64.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.8b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
✓	5.7b	(/.f64 (*.f64 b1 b2) a2)

series41.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

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

rewrite12.0ms (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:

4.0ms	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
3.0ms	(/.f64 (*.f64 b1 b2) a2)

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
669×	`associate-/l*_binary64`
503×	`associate-/l/_binary64`
500×	`associate-*l/_binary64`
479×	`associate-/r/_binary64`

Counts

157 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1908
1	291	1776
2	1078	1770
3	4951	1770
4	5016	1770

prune85.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	121	9	130

Error

Counts

130 → 9

Alt Table

Status	Error	Program
	9.9b	(.f64 a1 (/.f64 1 (/.f64 (.f64 b1 b2) a2)))
	10.8b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	9.9b	(/.f64 a1 (/.f64 1 (/.f64 a2 (*.f64 b1 b2))))
	10.3b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	10.6b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	23.0b	(*.f64 (/.f64 1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 a1 (/.f64 b2 (sqrt.f64 a2))))
▶	9.0b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (*.f64 b1 b2)) (/.f64 (cbrt.f64 a1) (/.f64 1 a2)))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 1874 to 538 computations (71.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 a1) (cbrt.f64 a1))
✓	0.6b	(cbrt.f64 a1)
✓	4.8b	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (.f64 b1 b2))
✓	5.9b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (*.f64 b1 b2)) (/.f64 (cbrt.f64 a1) (/.f64 1 a2)))

series716.0ms (13.8%)

Counts

4 → 108

Calls

4 calls:

607.0ms	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (.f64 b1 b2))
41.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (*.f64 b1 b2)) (/.f64 (cbrt.f64 a1) (/.f64 1 a2)))
37.0ms	(*.f64 (cbrt.f64 a1) (cbrt.f64 a1))
30.0ms	(cbrt.f64 a1)

rewrite67.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
133×	`add-exp-log_binary64`
113×	`add-sqr-sqrt_binary64`
89×	`associate-r_binary64`
85×	`*-un-lft-identity_binary64`

Counts

4 → 227

Calls

4 calls:

25.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (*.f64 b1 b2)) (/.f64 (cbrt.f64 a1) (/.f64 1 a2)))
6.0ms	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (.f64 b1 b2))
4.0ms	(*.f64 (cbrt.f64 a1) (cbrt.f64 a1))
1.0ms	(cbrt.f64 a1)

simplify197.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

361×	`fma-neg_binary64`
316×	`associate-l_binary64`
285×	`associate-r_binary64`
282×	`fma-def_binary64`
276×	`associate-*r/_binary64`

Counts

335 → 338

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	6082
1	611	4637
2	3106	4474
3	3846	4355
4	4782	4355
5	4972	4355

prune211.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	373	1	374
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	374	9	383

Error

Counts

383 → 9

Alt Table

Status	Error	Program
	9.9b	(.f64 a1 (/.f64 1 (/.f64 (.f64 b1 b2) a2)))
	10.8b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	10.3b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	10.6b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	23.0b	(*.f64 (/.f64 1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 a1 (/.f64 b2 (sqrt.f64 a2))))
✓	9.0b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (*.f64 b1 b2)) (/.f64 (cbrt.f64 a1) (/.f64 1 a2)))
▶	9.4b	(/.f64 a1 (/.f64 (*.f64 b2 b1) a2))
	12.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 9100 to 3406 computations (62.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.8b	(/.f64 a1 (/.f64 (*.f64 b2 b1) a2))
✓	5.7b	(/.f64 (*.f64 b2 b1) a2)

series40.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f64 a1 (/.f64 (*.f64 b2 b1) a2))
12.0ms	(/.f64 (*.f64 b2 b1) 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 b2 b1) a2))
3.0ms	(/.f64 (*.f64 b2 b1) a2)

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
650×	`associate-/l*_binary64`
479×	`associate-/l/_binary64`
478×	`associate-*l/_binary64`
452×	`associate-/r/_binary64`

Counts

121 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1656
1	290	1524
2	1059	1518
3	4788	1518
4	4995	1518

prune62.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	105	7	112

Error

Counts

112 → 7

Alt Table

Status	Error	Program
	10.3b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	10.6b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	9.9b	(.f64 a1 (/.f64 1 (/.f64 (.f64 b1 b2) a2)))
	9.8b	(/.f64 (/.f64 a1 b2) (/.f64 b1 a2))
✓	9.0b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (*.f64 b1 b2)) (/.f64 (cbrt.f64 a1) (/.f64 1 a2)))
	12.5b	(/.f64 (/.f64 a1 b1) (/.f64 b2 a2))
	11.3b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 1434 to 378 computations (73.6% saved)

regimes917.0ms (17.7%)

Accuracy

Total 4.8b remaining (99.4%)

Threshold costs 0b (0%)

Counts

56 → 5

Compiler

Compiled 6857 to 4051 computations (40.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	105
1	43	105
2	42	105

end393.0ms (7.6%)

Compiler: Compiled 538 to 284 computations (47.2% saved)

Details

analyze861.0ms (16.6%)

sample1.2s (23.3%)

simplify16.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series28.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify87.0ms (1.7%)

prune33.0ms (0.6%)

localize5.0ms (0.1%)

series41.0ms (0.8%)

rewrite12.0ms (0.2%)

simplify77.0ms (1.5%)

prune85.0ms (1.6%)

localize10.0ms (0.2%)

series716.0ms (13.8%)

rewrite67.0ms (1.3%)

simplify197.0ms (3.8%)

prune211.0ms (4.1%)

localize6.0ms (0.1%)

series40.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify71.0ms (1.4%)

prune62.0ms (1.2%)

regimes917.0ms (17.7%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end393.0ms (7.6%)

Profiling