Details

analyze100.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
37.5%	43.7%	18.8%	7
50%	31.2%	18.8%	8
56.2%	20.3%	23.5%	9
61.7%	14.8%	23.5%	10
64.4%	9.8%	25.9%	11
66.9%	7.2%	25.9%	12
68.2%	4.8%	27%	13
69.4%	3.6%	27%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample832.0ms (34.4%)

Symmetry

(sort a b)

Results

781.0ms	8256×	body	128	valid
11.0ms	130×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify14.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

284×	`fma-def_binary64`
35×	`associate-l_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`
19×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

16.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.9b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))

Compiler

Compiled 38 to 20 computations (47.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	6.8b	(.f64 (.f64 (*.f64 a a) b) b)
✓	9.5b	(.f64 (.f64 a a) b)

series18.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.f64 (.f64 (*.f64 a a) b) b)
8.0ms	(.f64 (.f64 a a) b)

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f64 (.f64 (*.f64 a a) b) b)
4.0ms	(.f64 (.f64 a a) b)

simplify80.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
359×	`unswap-sqr_binary64`
354×	`associate-/l/_binary64`
272×	`sqr-pow_binary64`
262×	`associate-/r/_binary64`

Counts

92 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	983
1	142	854
2	480	830
3	782	812
4	1506	801
5	2460	801
6	4674	801
7	4916	801

prune53.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Error

0.0b

Counts

57 → 7

Alt Table

Status	Error	Program
▶	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	21.2b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	25.6b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	21.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	23.8b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	23.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	7.1b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))

Compiler

Compiled 890 to 318 computations (64.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 a b) (*.f64 a b))

series11.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(*.f64 (*.f64 a b) (*.f64 a b))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`pow1_binary64`
17×	`pow-prod-down_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

1 → 36

Calls

1 calls:

5.0ms

(*.f64 (*.f64 a b) (*.f64 a b))

simplify80.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

654×	`associate-l_binary64`
551×	`fma-def_binary64`
352×	`associate-r_binary64`
341×	`associate-/l*_binary64`
311×	`associate-/l/_binary64`

Counts

60 → 34

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	613
1	92	508
2	315	474
3	1009	474
4	1436	372
5	2353	372
6	4908	372
7	4999	372
8	4954	372

prune28.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	33	8	41

Error

0.0b

Counts

41 → 8

Alt Table

Status	Error	Program
▶	4.6b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	7.1b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	21.2b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	25.6b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	21.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	23.8b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	23.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))

Compiler

Compiled 596 to 248 computations (58.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 b (.f64 a b))
✓	4.5b	(.f64 a (.f64 b (*.f64 a b)))

series18.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 a (.f64 b (*.f64 a b)))
7.0ms	(.f64 b (.f64 a b))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(.f64 a (.f64 b (*.f64 a b)))
4.0ms	(.f64 b (.f64 a b))

simplify90.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
427×	`associate-/l/_binary64`
369×	`associate-/l*_binary64`
361×	`sqr-pow_binary64`
358×	`associate-/r/_binary64`

Counts

91 → 62

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	993
1	134	828
2	417	804
3	652	792
4	1254	683
5	2059	683
6	4787	683
7	4948	683
8	4984	683

prune50.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	60	10	70

Error

0.0b

Counts

70 → 10

Alt Table

Status	Error	Program
	20.2b	(neg.f64 (.f64 a (.f64 (sqrt.f64 b) (.f64 (sqrt.f64 b) (.f64 a b)))))
	21.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	4.6b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	7.1b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	25.6b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	15.1b	(neg.f64 (.f64 a (.f64 1 (.f64 a (.f64 b b)))))
▶	5.2b	(neg.f64 (.f64 a (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 a b)))))
	23.8b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	23.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))

Compiler

Compiled 1005 to 403 computations (59.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 b) (.f64 a b))
✓	0.4b	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
✓	0.7b	(cbrt.f64 b)
✓	4.5b	(.f64 a (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 a b))))

series401.0ms (16.6%)

Counts

4 → 72

Calls

4 calls:

308.0ms	(.f64 (cbrt.f64 b) (.f64 a b))
35.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
34.0ms	(cbrt.f64 b)
24.0ms	(.f64 a (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 a b))))

rewrite29.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`pow1_binary64`
40×	`add-exp-log_binary64`
27×	`pow-prod-down_binary64`
26×	`cbrt-unprod_binary64`
26×	`add-cbrt-cube_binary64`

Counts

4 → 113

Calls

4 calls:

11.0ms	(.f64 a (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 a b))))
6.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
4.0ms	(.f64 (cbrt.f64 b) (.f64 a b))
1.0ms	(cbrt.f64 b)

simplify102.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1019×	`fma-def_binary64`
590×	`*-commutative_binary64`
348×	`associate-r_binary64`
348×	`swap-sqr_binary64`
318×	`associate-l_binary64`

Counts

185 → 157

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2055
1	300	1760
2	1206	1642
3	2324	1617
4	4366	1617
5	4983	1617

prune143.0ms (5.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	192	11	203

Error

0.0b

Counts

203 → 11

Alt Table

Status	Error	Program
	20.2b	(neg.f64 (.f64 a (.f64 (sqrt.f64 b) (.f64 (sqrt.f64 b) (.f64 a b)))))
	21.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	5.2b	(neg.f64 (.f64 a (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 a b)))))
	5.3b	(neg.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (cbrt.f64 a) (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (cbrt.f64 b) (*.f64 a b))))))
✓	4.6b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	7.1b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	25.6b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	15.1b	(neg.f64 (.f64 a (.f64 1 (.f64 a (.f64 b b)))))
	23.8b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	23.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))

Compiler

Compiled 3962 to 1092 computations (72.4% saved)

regimes202.0ms (8.4%)

Accuracy

Total 0.3b remaining (86.3%)

Threshold costs 0.3b (86.3%)

Counts

48 → 1

Compiler

Compiled 4118 to 2199 computations (46.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
2	14	9
3	15	9
4	15	9

end106.0ms (4.4%)

Remove: (sort a b)
Compiler: Compiled 175 to 110 computations (37.1% saved)

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

Details

analyze100.0ms (4.1%)

sample832.0ms (34.4%)

simplify14.0ms (0.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series18.0ms (0.8%)

rewrite13.0ms (0.6%)

simplify80.0ms (3.3%)

prune53.0ms (2.2%)

localize4.0ms (0.2%)

series11.0ms (0.4%)

rewrite7.0ms (0.3%)

simplify80.0ms (3.3%)

prune28.0ms (1.2%)

localize5.0ms (0.2%)

series18.0ms (0.8%)

rewrite12.0ms (0.5%)

simplify90.0ms (3.7%)

prune50.0ms (2.1%)

localize8.0ms (0.3%)

series401.0ms (16.6%)

rewrite29.0ms (1.2%)

simplify102.0ms (4.2%)

prune143.0ms (5.9%)

regimes202.0ms (8.4%)

simplify2.0ms (0.1%)

end106.0ms (4.4%)

Profiling

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12