Details

analyze102.0ms (3.8%)

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)

sample825.0ms (31.2%)

Symmetry

(sort a b)

Results

765.0ms	8256×	body	128	valid
20.0ms	142×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify15.0ms (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

16.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.1b	(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
✓	2.6b	(.f64 (.f64 (*.f64 a a) b) b)
✓	12.8b	(.f64 (.f64 a a) b)

series20.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 (*.f64 a a) b) b)
8.0ms	(.f64 (.f64 a a) b)

rewrite16.0ms (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:

8.0ms	(.f64 (.f64 a a) b)
6.0ms	(.f64 (.f64 (*.f64 a a) b) b)

simplify81.0ms (3.1%)

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

prune47.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	9	57

Error

0.0b

Counts

57 → 9

Alt Table

Status	Error	Program
▶	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	21.3b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	16.1b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	23.5b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	2.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	17.8b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	16.4b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a a) b)) (cbrt.f64 (.f64 (.f64 a a) b))) (cbrt.f64 (.f64 (*.f64 a a) b))) b))
	21.8b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	27.9b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 950 to 342 computations (64% 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))

series15.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(*.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%)

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

prune30.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	33	10	43

Error

0.0b

Counts

43 → 10

Alt Table

Status	Error	Program
	14.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	17.8b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	21.3b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	16.1b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
▶	2.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	4.5b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	23.5b	(neg.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a b) (.f64 a b)) (.f64 (.f64 a b) (.f64 a b))) (.f64 (.f64 a b) (*.f64 a b)))))
	21.8b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	27.9b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 662 to 268 computations (59.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a (.f64 a b))
✓	2.6b	(.f64 (.f64 a (*.f64 a b)) b)

series20.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 a (*.f64 a b)) b)
8.0ms	(.f64 a (.f64 a b))

rewrite13.0ms (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 (.f64 a (*.f64 a b)) b)
4.0ms	(.f64 a (.f64 a b))

simplify81.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

613×	`associate-/l/_binary64`
601×	`fma-def_binary64`
310×	`unswap-sqr_binary64`
264×	`sqr-pow_binary64`
240×	`*-commutative_binary64`

Counts

91 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	982
1	152	841
2	538	805
3	804	795
4	1566	689
5	2640	689
6	4984	689
7	5171	689

prune48.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	3	4	7
Picked	0	1	1
Done	1	1	2
Total	64	9	73

Error

0.0b

Counts

73 → 9

Alt Table

Status	Error	Program
	14.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	17.8b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	17.8b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a b)) (sqrt.f64 b)) (sqrt.f64 b)))
	4.5b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
▶	3.3b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a b)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	21.3b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	16.1b	(neg.f64 (.f64 (pow.f64 (.f64 (*.f64 a a) b) 1) b))
✓	2.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))

Compiler

Compiled 989 to 381 computations (61.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
✓	0.6b	(cbrt.f64 b)
✓	0.6b	(.f64 (.f64 (.f64 a (.f64 a b)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))
✓	2.2b	(.f64 (.f64 a (.f64 a b)) (.f64 (cbrt.f64 b) (cbrt.f64 b)))

series447.0ms (16.9%)

Counts

4 → 72

Calls

4 calls:

352.0ms	(.f64 (.f64 a (.f64 a b)) (.f64 (cbrt.f64 b) (cbrt.f64 b)))
38.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
30.0ms	(cbrt.f64 b)
27.0ms	(.f64 (.f64 (.f64 a (.f64 a b)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))

rewrite37.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64`
56×	`add-exp-log_binary64`
39×	`pow-prod-down_binary64`
38×	`cbrt-unprod_binary64`
38×	`prod-exp_binary64`

Counts

4 → 123

Calls

4 calls:

13.0ms	(.f64 (.f64 (.f64 a (.f64 a b)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))
8.0ms	(.f64 (.f64 a (.f64 a b)) (.f64 (cbrt.f64 b) (cbrt.f64 b)))
4.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
1.0ms	(cbrt.f64 b)

simplify142.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1052×	`fma-def_binary64`
395×	`associate-l_binary64`
356×	`unswap-sqr_binary64`
338×	`associate-r_binary64`
326×	`log-prod_binary64`

Counts

195 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2659
1	311	2076
2	1327	1848
3	2346	1821
4	4143	1821
5	4915	1821

prune170.0ms (6.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	199	8	207

Error

0.0b

Counts

207 → 8

Alt Table

Status	Error	Program
	3.4b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a (.f64 a b)) (.f64 (cbrt.f64 b) (cbrt.f64 b)))) (cbrt.f64 (.f64 (.f64 a (.f64 a b)) (.f64 (cbrt.f64 b) (cbrt.f64 b))))) (cbrt.f64 (.f64 (.f64 a (.f64 a b)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))))) (cbrt.f64 b)))
	16.1b	(neg.f64 (.f64 (pow.f64 (.f64 (*.f64 a a) b) 1) b))
	14.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	17.8b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a b)) (sqrt.f64 b)) (sqrt.f64 b)))
	1.8b	(neg.f64 (.f64 (.f64 a (.f64 (.f64 a b) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))) (cbrt.f64 b)))
✓	2.7b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	4.5b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))

Compiler

Compiled 4047 to 1109 computations (72.6% saved)

regimes332.0ms (12.5%)

Accuracy

Total 0.3b remaining (84.1%)

Threshold costs 0.3b (84.1%)

Counts

73 → 1

Compiler

Compiled 6917 to 3736 computations (46% 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

end89.0ms (3.3%)

Remove: (sort a b)
Compiler: Compiled 159 to 84 computations (47.2% 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

analyze102.0ms (3.8%)

sample825.0ms (31.2%)

simplify15.0ms (0.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series20.0ms (0.7%)

rewrite16.0ms (0.6%)

simplify81.0ms (3.1%)

prune47.0ms (1.8%)

localize4.0ms (0.2%)

series15.0ms (0.6%)

rewrite7.0ms (0.3%)

simplify80.0ms (3%)

prune30.0ms (1.1%)

localize7.0ms (0.2%)

series20.0ms (0.7%)

rewrite13.0ms (0.5%)

simplify81.0ms (3.1%)

prune48.0ms (1.8%)

localize10.0ms (0.4%)

series447.0ms (16.9%)

rewrite37.0ms (1.4%)

simplify142.0ms (5.4%)

prune170.0ms (6.4%)

regimes332.0ms (12.5%)

simplify2.0ms (0.1%)

end89.0ms (3.3%)

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