Details

analyze10.0ms (0.2%)

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)

sample1.1s (23.9%)

Results

853.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify163.0ms (3.7%)

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%)

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 (0.1%)

Counts

2 → 12

Calls

2 calls:

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

rewrite302.0ms (6.8%)

Algorithm

2×	egg-rewrite

Rules

53×	`egg`
48×	`egg`

Counts

2 → 101

Calls

2 calls:

158.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
142.0ms	(*.f64 2 (pow.f64 x 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	122	6
2	1214	6
3	4880	6
4	6252	6
0	5	7
1	102	7
2	1010	7
3	4691	7
4	5759	7

simplify12.0ms (0.3%)

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

113 → 101

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

prune88.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

0.1b

Counts

102 → 7

Alt Table

Status	Error	Program
✓	27.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	32.2b	(*.f64 (sqrt.f64 2) x)
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	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))

Compiler

Compiled 1184 to 903 computations (23.7% saved)

localize10.0ms (0.2%)

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)

series315.0ms (7.1%)

Counts

4 → 48

Calls

4 calls:

304.0ms	(pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)
4.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
4.0ms	(.f64 x (.f64 x (sqrt.f64 2)))
3.0ms	(*.f64 x (sqrt.f64 2))

rewrite252.0ms (5.7%)

Algorithm

4×	egg-rewrite

Rules

59×	`egg`
54×	`egg`
44×	`egg`
31×	`egg`

Counts

4 → 188

Calls

4 calls:

83.0ms	(*.f64 x (sqrt.f64 2))
80.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
45.0ms	(pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/2)
42.0ms	(.f64 x (.f64 x (sqrt.f64 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	166	7
2	1672	7
3	4887	7
0	5	6
1	99	6
2	1029	6
3	4823	6
4	5948	6
0	10	6
1	204	6
2	1897	6
3	4961	6
4	4945	6
0	6	9
1	120	9
2	1293	9
3	4948	9

simplify116.0ms (2.6%)

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

236 → 187

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

prune107.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

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

Compiler

Compiled 3024 to 2521 computations (16.6% saved)

localize7.0ms (0.2%)

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))))

series38.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

29.0ms	(*.f64 x (pow.f64 2 1/4))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

rewrite224.0ms (5.1%)

Algorithm

2×	egg-rewrite

Rules

39×	`egg`
35×	`egg`

Counts

2 → 74

Calls

2 calls:

142.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))
81.0ms	(*.f64 x (pow.f64 2 1/4))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	207	6
2	1721	6
3	4888	6
0	6	7
1	127	7
2	1259	7
3	4822	7
4	6167	7

simplify170.0ms (3.8%)

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

98 → 74

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

prune46.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	5	5
Picked	0	1	1
Done	1	0	1
Total	74	7	81

Error

0.0b

Counts

81 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/12) x))))
	32.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
	43.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

Compiler

Compiled 1097 to 951 computations (13.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/12) x))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/12) x))))
✓	0.3b	(*.f64 (pow.f64 2 1/12) x)

series622.0ms (14.1%)

Counts

3 → 24

Calls

3 calls:

584.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/12) x))
25.0ms	(*.f64 (pow.f64 2 1/12) x)
12.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/12) x))))

rewrite183.0ms (4.1%)

Algorithm

3×	egg-rewrite

Rules

41×	`egg`
39×	`egg`
33×	`egg`

Counts

3 → 113

Calls

3 calls:

82.0ms	(*.f64 (pow.f64 2 1/12) x)
52.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/12) x))))
47.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/12) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	126	7
2	1286	7
3	4933	7
4	6374	7
0	12	23
1	246	13
2	2314	13
3	5153	13
0	9	14
1	184	7
2	1836	7
3	5260	7

simplify202.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1554×	`fabs-mul_binary64`
927×	`unswap-sqr_binary64`
705×	`sqr-pow_binary64`
472×	`*-commutative_binary64`
325×	`fabs-sqr_binary64`

Counts

137 → 115

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	444
1	30	444
2	72	444
3	209	444
4	826	444
5	1331	444
6	1545	444
7	1554	444
8	1669	444
9	1799	444
10	1939	444
11	2030	444
12	2215	444
13	2434	444
14	2569	444
15	2766	444
16	2984	444
17	3216	444
18	3469	444
19	3850	444
20	4001	444
21	5472	444

prune145.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	115	7	122

Error

0.0b

Counts

122 → 7

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/12) x))))
	32.9b	(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
	43.3b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 (.f64 x (pow.f64 2 1/4))))

Compiler

Compiled 1970 to 1768 computations (10.3% saved)

regimes237.0ms (5.4%)

Accuracy

Total 0.4b remaining (92.5%)

Threshold costs 0.4b (92.5%)

Counts

27 → 1

Compiler

Compiled 1190 to 1022 computations (14.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`fabs-mul_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	18	23
2	23	23
3	23	23

end94.0ms (2.1%)

Compiler: Compiled 92 to 82 computations (10.9% saved)

Details

analyze10.0ms (0.2%)

sample1.1s (23.9%)

simplify163.0ms (3.7%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite302.0ms (6.8%)

simplify12.0ms (0.3%)

prune88.0ms (2%)

localize10.0ms (0.2%)

series315.0ms (7.1%)

rewrite252.0ms (5.7%)

simplify116.0ms (2.6%)

prune107.0ms (2.4%)

localize7.0ms (0.2%)

series38.0ms (0.9%)

rewrite224.0ms (5.1%)

simplify170.0ms (3.8%)

prune46.0ms (1%)

localize9.0ms (0.2%)

series622.0ms (14.1%)

rewrite183.0ms (4.1%)

simplify202.0ms (4.6%)

prune145.0ms (3.3%)

regimes237.0ms (5.4%)

simplify2.0ms (0%)

end94.0ms (2.1%)

Profiling