Details

analyze108.0ms (2.5%)

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
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.3s (29.9%)

Results

671.0ms	6443×	body	128	valid
214.0ms	638×	body	1024	valid
171.0ms	706×	body	512	valid
78.0ms	463×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify204.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

15.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.6b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶	15.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	15.6b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series18.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite99.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

65× egg-rr

Counts

2 → 65

Calls

2 calls:

98.0ms	((fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1) (/.f64 (+.f64 x -1) (+.f64 1 y)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	193	24
2	2481	24
3	4892	24
4	5106	24
0	0	0
1	0	0

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
486×	`associate--l+_binary64`
453×	`times-frac_binary64`
420×	`associate--r+_binary64`
353×	`associate-+l+_binary64`

Counts

113 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1015
1	233	980
2	818	936
3	3450	893
4	4788	893
5	5485	893

prune71.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	103	3	106

Error

0.0b

Counts

106 → 3

Alt Table

Status	Error	Program
▶	23.6b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
	29.8b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	15.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 1815 to 1272 computations (29.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) y)
✓	2.7b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
✓	7.5b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

series27.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

13.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
9.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
4.0ms	(*.f64 (-.f64 1 x) y)

rewrite140.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

124× egg-rr

Counts

3 → 124

Calls

2 calls:

137.0ms	((/.f64 (.f64 (-.f64 1 x) y) (+.f64 y 1)) (-.f64 1 (/.f64 (.f64 (-.f64 1 x) y) (+.f64 y 1))) (*.f64 (-.f64 1 x) y))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	208	36
2	2931	36
3	4795	36
4	4817	36
5	5156	36
0	0	0
1	0	0

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-neg_binary64`
474×	`associate--l+_binary64`
408×	`associate--r+_binary64`
345×	`associate-+l+_binary64`
329×	`fma-def_binary64`

Counts

184 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1079
1	253	1058
2	858	1031
3	3665	1018
4	4771	1018
5	4968	1018

prune99.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	169	3	172

Error

0.0b

Counts

172 → 3

Alt Table

Status	Error	Program
✓	23.6b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶	29.8b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	15.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 2979 to 2077 computations (30.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (*.f64 y y))
✓	2.2b	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
✓	5.9b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	6.5b	(/.f64 x (*.f64 y y))

series87.0ms (2.1%)

Counts

4 → 84

Calls

4 calls:

36.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
27.0ms	(/.f64 x (*.f64 y y))
21.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
2.0ms	(/.f64 1 (*.f64 y y))

rewrite107.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

169× egg-rr

Counts

4 → 169

Calls

2 calls:

103.0ms	((/.f64 x (.f64 y y)) (-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)) (/.f64 1 (*.f64 y y)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	312	47
2	4739	47
3	5147	47
0	0	0
1	0	0

simplify184.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

608×	`div-sub_binary64`
541×	`times-frac_binary64`
517×	`unsub-neg_binary64`
383×	`neg-mul-1_binary64`
365×	`sub-neg_binary64`

Counts

253 → 195

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	1218
1	91	1062
2	224	1014
3	530	1008
4	1534	960
5	3793	960
6	4876	960
7	4938	960
8	4107	960
9	4670	960
10	4878	960
11	4952	960

prune148.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	193	5	198

Error

Counts

198 → 5

Alt Table

Status	Error	Program
✓	23.6b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
	37.1b	(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (cbrt.f64 (pow.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y)) 3)))
▶	30.0b	(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))) 3))
✓	29.8b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	15.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 5338 to 2912 computations (45.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))
✓	5.9b	(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))) 3))
	6.5b	(/.f64 x (*.f64 y y))
✓	17.8b	(cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y)))

series77.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

38.0ms

(cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y)))

28.0ms

(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))) 3))

11.0ms

(+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))

rewrite84.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

109× egg-rr

Counts

3 → 109

Calls

2 calls:

81.0ms

((cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))) (-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))) 3)) (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	53
1	361	51
2	4765	51
3	5145	51
0	0	0
1	0	0

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

345×	`cancel-sign-sub-inv_binary64`
326×	`fma-neg_binary64`
243×	`sub-neg_binary64`
204×	`distribute-rgt-in_binary64`
191×	`fma-def_binary64`

Counts

181 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	235	3082
1	767	2835
2	2682	2476
3	4913	2470
4	5027	2470

prune188.0ms (4.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	216	5	221

Error

Counts

221 → 5

Alt Table

Status	Error	Program
✓	23.6b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
	37.1b	(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (cbrt.f64 (pow.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y)) 3)))
✓	30.0b	(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 y -2) (/.f64 (+.f64 x -1) y))) 3))
✓	29.8b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	15.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 7822 to 5044 computations (35.5% saved)

regimes914.0ms (21.5%)

Accuracy

Total 0.1b remaining (71.3%)

Threshold costs 0.1b (71.3%)

Counts

103 → 3

Compiler

Compiled 9653 to 6388 computations (33.8% saved)

bsearch30.0ms (0.7%)

Steps

Iters	Range		Point
9	8.778871274599725	839681.9684021454	449605.74478200584
3	-424883597567483.56	-304245671921634.56	-311785542274500.1

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`distribute-rgt-neg-in_binary64`
22×	`cancel-sign-sub-inv_binary64`
18×	`distribute-lft-neg-in_binary64`
15×	`distribute-neg-in_binary64`
14×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	74
1	42	74
2	58	74
3	79	74
4	100	74
5	130	74
6	146	74
7	152	74
8	148	74

end99.0ms (2.3%)

Compiler: Compiled 196 to 133 computations (32.1% saved)

Details

analyze108.0ms (2.5%)

sample1.3s (29.9%)

simplify204.0ms (4.8%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series18.0ms (0.4%)

rewrite99.0ms (2.3%)

simplify71.0ms (1.7%)

prune71.0ms (1.7%)

localize6.0ms (0.1%)

series27.0ms (0.6%)

rewrite140.0ms (3.3%)

simplify73.0ms (1.7%)

prune99.0ms (2.3%)

localize10.0ms (0.2%)

series87.0ms (2.1%)

rewrite107.0ms (2.5%)

simplify184.0ms (4.3%)

prune148.0ms (3.5%)

localize18.0ms (0.4%)

series77.0ms (1.8%)

rewrite84.0ms (2%)

simplify107.0ms (2.5%)

prune188.0ms (4.4%)

regimes914.0ms (21.5%)

bsearch30.0ms (0.7%)

simplify5.0ms (0.1%)

end99.0ms (2.3%)

Profiling