Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample2.1s (41.6%)

Results

929.0ms	2287×	body	1024	valid
679.0ms	4402×	body	128	valid
322.0ms	1012×	body	512	valid
107.0ms	555×	body	256	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

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

19.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	2.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series46.0ms (0.9%)

Counts

4 → 8

Calls

4 calls:

15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(/.f64 1 (sqrt.f64 x))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite341.0ms (6.9%)

Algorithm

4×	egg-rewrite

Rules

125×	`egg`
65×	`egg`
43×	`egg`
33×	`egg`

Counts

4 → 266

Calls

4 calls:

102.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
80.0ms	(sqrt.f64 (+.f64 x 1))
79.0ms	(/.f64 1 (sqrt.f64 x))
75.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	205	13
2	2570	13
3	4757	13
4	4948	13
0	5	6
1	97	4
2	1003	4
3	4726	4
4	4846	4
0	6	9
1	128	7
2	1442	7
3	4864	7
4	5078	7
0	5	6
1	102	6
2	1131	6
3	4620	6
4	6219	6

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-neg_binary64`
743×	`cancel-sign-sub-inv_binary64`
601×	`distribute-rgt-neg-in_binary64`
443×	`fma-def_binary64`
382×	`unsub-neg_binary64`

Counts

274 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	94
1	79	86
2	203	76
3	566	64
4	1706	64
5	3239	64
6	4401	64
7	5119	64

prune344.0ms (6.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	264	12	276
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	12	277

Error

19.2b

Counts

277 → 12

Alt Table

Status	Error	Program
	29.0b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
	29.9b	(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	25.2b	(/.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
▶	19.6b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	30.4b	(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
	29.2b	(fma.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 x -1/2))
	29.5b	(fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	29.8b	(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	29.2b	(+.f64 (fma.f64 1 (pow.f64 x -1/2) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	29.2b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1) (pow.f64 (+.f64 1 x) -1/2)))
	29.5b	(+.f64 (fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	29.3b	(+.f64 (fma.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))

Compiler

Compiled 6305 to 5060 computations (19.7% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 x) -1/2)
✓	2.6b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

series11.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
4.0ms	(pow.f64 (+.f64 1 x) -1/2)

rewrite150.0ms (3%)

Algorithm

2×	egg-rewrite

Rules

91×	`egg`
27×	`egg`

Counts

2 → 118

Calls

2 calls:

80.0ms	(pow.f64 (+.f64 1 x) -1/2)
67.0ms	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	183	13
2	2175	13
3	6355	13
0	6	7
1	129	7
2	1404	7
3	4835	7
4	5004	7

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

542×	`cancel-sign-sub-inv_binary64`
484×	`times-frac_binary64`
431×	`fma-neg_binary64`
353×	`sub-neg_binary64`
277×	`associate-/l*_binary64`

Counts

142 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	797
1	241	769
2	668	583
3	1896	471
4	4291	471
5	4966	471

prune164.0ms (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	170	3	173

Error

0.1b

Counts

173 → 3

Alt Table

Status	Error	Program
	33.2b	(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
	43.5b	(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
▶	25.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))

Compiler

Compiled 3908 to 3215 computations (17.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.1b	(pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)
✓	0.2b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2)
✓	15.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))

series53.0ms (1.1%)

Counts

4 → 18

Calls

4 calls:

19.0ms	(pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)
19.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2)
8.0ms	(-.f64 (pow.f64 x -1/2) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))
7.0ms	(sqrt.f64 (+.f64 1 x))

rewrite331.0ms (6.7%)

Algorithm

4×	egg-rewrite

Rules

111×	`egg`
43×	`egg`
30×	`egg`
29×	`egg`

Counts

4 → 213

Calls

4 calls:

128.0ms	(-.f64 (pow.f64 x -1/2) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))
79.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2)
76.0ms	(sqrt.f64 (+.f64 1 x))
44.0ms	(pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	248	13
2	2704	13
3	4797	13
4	4814	13
5	4862	13
0	9	9
1	194	7
2	1933	7
3	4974	7
4	4814	7
0	7	7
1	149	7
2	1603	7
3	4933	7
0	5	6
1	101	6
2	1144	6
3	4635	6
4	4943	6

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

426×	`distribute-rgt-neg-in_binary64`
413×	`cancel-sign-sub-inv_binary64`
402×	`sub-neg_binary64`
354×	`distribute-lft-neg-in_binary64`
325×	`associate-l_binary64`

Counts

231 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	222
1	155	202
2	436	185
3	1226	174
4	3106	174
5	4498	174
6	4960	174
7	4998	174

prune168.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	239	3	242

Error

0.1b

Counts

242 → 3

Alt Table

Status	Error	Program
▶	33.2b	(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
	43.5b	(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
✓	25.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))

Compiler

Compiled 4787 to 3961 computations (17.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 -3/8 x))
✓	0.1b	(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
✓	0.2b	(/.f64 (pow.f64 x -1/2) x)

series21.0ms (0.4%)

Counts

3 → 12

Calls

3 calls:

12.0ms	(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
7.0ms	(/.f64 (pow.f64 x -1/2) x)
2.0ms	(+.f64 1/2 (/.f64 -3/8 x))

rewrite227.0ms (4.6%)

Algorithm

3×	egg-rewrite

Rules

99×	`egg`
86×	`egg`
38×	`egg`

Counts

3 → 223

Calls

3 calls:

95.0ms	(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
86.0ms	(/.f64 (pow.f64 x -1/2) x)
42.0ms	(+.f64 1/2 (/.f64 -3/8 x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	112	4
2	1267	4
3	4923	4
4	5224	4
0	10	16
1	237	13
2	2947	13
3	4951	13
4	5287	13
0	6	7
1	139	7
2	1697	7
3	4896	7

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
11×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l-_binary64`

Counts

235 → 224

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	69
1	20	69
2	29	69
3	45	69
4	59	69
5	77	69
6	92	69
7	101	69
8	108	69
9	76	69

prune140.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	224	3	227

Error

Counts

227 → 3

Alt Table

Status	Error	Program
✓	25.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))
	33.2b	(/.f64 (pow.f64 x -1/2) (/.f64 x (+.f64 1/2 (/.f64 -3/8 x))))
	33.1b	(*.f64 (pow.f64 x -3/2) (+.f64 1/2 (/.f64 -3/8 x)))

Compiler

Compiled 3797 to 2902 computations (23.6% saved)

regimes440.0ms (8.9%)

Accuracy

Total 0.3b remaining (72.8%)

Threshold costs 0.3b (72.8%)

Counts

136 → 2

Compiler

Compiled 4778 to 3972 computations (16.9% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	79
1	41	79
2	51	79
3	56	79
4	58	79
5	56	79

end150.0ms (3%)

Compiler: Compiled 141 to 116 computations (17.7% saved)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

Details

analyze1.0ms (0%)

sample2.1s (41.6%)

simplify15.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series46.0ms (0.9%)

rewrite341.0ms (6.9%)

simplify74.0ms (1.5%)

prune344.0ms (6.9%)

localize12.0ms (0.2%)

series11.0ms (0.2%)

rewrite150.0ms (3%)

simplify69.0ms (1.4%)

prune164.0ms (3.3%)

localize10.0ms (0.2%)

series53.0ms (1.1%)

rewrite331.0ms (6.7%)

simplify97.0ms (1.9%)

prune168.0ms (3.4%)

localize8.0ms (0.2%)

series21.0ms (0.4%)

rewrite227.0ms (4.6%)

simplify14.0ms (0.3%)

prune140.0ms (2.8%)

regimes440.0ms (8.9%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end150.0ms (3%)

Profiling

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17