Details

analyze10.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.0s (38.6%)

Results

833.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify139.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	22	9
3	41	9
4	88	9
5	221	9
6	693	9
7	1098	9
8	1100	9
9	1248	9
10	1418	9
11	1600	9
12	1825	9
13	2110	9
14	2529	9
15	3094	9
16	3780	9
17	3998	9
18	4242	9
19	4324	9
20	4357	9
21	4378	9
22	4947	9

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

27.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	26.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series5.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
2.0ms	(*.f64 2 (pow.f64 x 2))

rewrite134.0ms (5.1%)

Algorithm

2×	batch-egg-rewrite

Rules

72× egg-rr

Counts

2 → 72

Calls

2 calls:

133.0ms	((sqrt.f64 (.f64 2 (pow.f64 x 2))) (.f64 2 (pow.f64 x 2)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1214	13
3	4880	13
4	6252	13
0	0	0
1	0	0

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

84 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune176.0ms (6.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Error

0.1b

Counts

75 → 7

Alt Table

Status	Error	Program
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	27.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
	43.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
▶	27.2b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
	32.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 856 to 669 computations (21.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 x (sqrt.f64 2)))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
✓	0.4b	(*.f64 x (sqrt.f64 2))
✓	26.2b	(pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)

series273.0ms (10.5%)

Counts

4 → 48

Calls

4 calls:

261.0ms	(pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)
4.0ms	(*.f64 x (sqrt.f64 2))
4.0ms	(.f64 x (.f64 x (sqrt.f64 2)))
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))

rewrite92.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

74× egg-rr

Counts

4 → 74

Calls

2 calls:

89.0ms	((pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2) (.f64 x (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)) (.f64 x (.f64 x (sqrt.f64 2))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	204	28
2	1897	28
3	4961	28
4	4945	28
0	0	0
1	0	0

simplify99.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

645×	`prod-exp_binary64`
635×	`log-prod_binary64`
485×	`fma-neg_binary64`
353×	`fma-def_binary64`
351×	`times-frac_binary64`

Counts

122 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	468
1	73	444
2	136	360
3	307	348
4	876	348
5	2068	348
6	4175	348
7	4468	348
8	4659	348
9	5710	348

prune40.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	64	7	71

Error

0.0b

Counts

71 → 7

Alt Table

Status	Error	Program
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	27.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	43.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
	32.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1026 to 890 computations (13.3% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (pow.f64 2 1/4))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

series37.0ms (1.4%)

Counts

2 → 24

Calls

2 calls:

28.0ms	(*.f64 x (pow.f64 2 1/4))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

rewrite43.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

39× egg-rr

Counts

2 → 39

Calls

2 calls:

42.0ms	((.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4)))) (*.f64 x (pow.f64 2 1/4)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	207	13
2	1721	13
3	4888	13
0	0	0
1	0	0

simplify147.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1895×	`fabs-mul_binary64`
701×	`sqr-pow_binary64`
464×	`cube-prod_binary64`
401×	`fabs-sqr_binary64`
361×	`pow-sqr_binary64`

Counts

63 → 41

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	276
1	19	276
2	35	276
3	68	276
4	167	276
5	483	276
6	603	276
7	822	276
8	914	276
9	984	276
10	1104	276
11	1266	276
12	1437	276
13	1689	276
14	2048	276
15	2502	276
16	3152	276
17	3635	276
18	3805	276
19	3919	276
20	3951	276
21	3965	276
22	4305	276
23	4794	276

prune25.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	41	7	48

Error

0.0b

Counts

48 → 7

Alt Table

Status	Error	Program
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	27.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	43.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
	32.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
▶	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 565 to 501 computations (11.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 (sqrt.f64 2) x)

rewrite73.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

37× egg-rr

Counts

1 → 37

Calls

2 calls:

72.0ms	((*.f64 (sqrt.f64 2) x))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	99	6
2	1029	6
3	4823	6
4	5948	6
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune18.0ms (0.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	37	7	44

Error

0.0b

Counts

44 → 7

Alt Table

Status	Error	Program
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	27.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	43.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
	32.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
✓	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 422 to 361 computations (14.5% saved)

regimes158.0ms (6%)

Accuracy

Total 0.4b remaining (92.5%)

Threshold costs 0.4b (92.5%)

Counts

18 → 1

Compiler

Compiled 742 to 622 computations (16.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	16	16
3	16	16

end83.0ms (3.2%)

Compiler: Compiled 76 to 66 computations (13.2% saved)

Details

analyze10.0ms (0.4%)

sample1.0s (38.6%)

simplify139.0ms (5.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series5.0ms (0.2%)

rewrite134.0ms (5.1%)

simplify11.0ms (0.4%)

prune176.0ms (6.8%)

localize9.0ms (0.3%)

series273.0ms (10.5%)

rewrite92.0ms (3.5%)

simplify99.0ms (3.8%)

prune40.0ms (1.5%)

localize7.0ms (0.3%)

series37.0ms (1.4%)

rewrite43.0ms (1.6%)

simplify147.0ms (5.6%)

prune25.0ms (1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite73.0ms (2.8%)

simplify6.0ms (0.2%)

prune18.0ms (0.7%)

regimes158.0ms (6%)

simplify3.0ms (0.1%)

end83.0ms (3.2%)

Profiling