Details

analyze145.0ms (3.5%)

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 (32.1%)

Results

737.0ms	6443×	body	128	valid
205.0ms	638×	body	1024	valid
188.0ms	706×	body	512	valid
77.0ms	463×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify198.0ms (4.7%)

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

series19.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
0.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify113.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
491×	`associate--l+_binary64`
425×	`associate--r+_binary64`
390×	`associate-+l+_binary64`
315×	`fma-def_binary64`

Counts

105 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2086
1	416	1897
2	1275	1850
3	4701	1850
4	5402	1850

prune71.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

0.0b

Counts

104 → 3

Alt Table

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

Compiler

Compiled 1870 to 1280 computations (31.6% 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))

series26.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

11.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
11.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
4.0ms	(*.f64 (-.f64 1 x) y)

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
26×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`

Counts

3 → 113

Calls

3 calls:

8.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
6.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
5.0ms	(*.f64 (-.f64 1 x) y)

simplify120.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

395×	`fma-neg_binary64`
383×	`cancel-sign-sub-inv_binary64`
261×	`sub-neg_binary64`
216×	`distribute-rgt-neg-in_binary64`
160×	`exp-prod_binary64`

Counts

173 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	3950
1	690	3374
2	2734	2924
3	4540	2924
4	4860	2924

prune138.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	202	3	205

Error

0.0b

Counts

205 → 3

Alt Table

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

Compiler

Compiled 4886 to 3480 computations (28.8% saved)

localize11.0ms (0.3%)

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))

series84.0ms (2%)

Counts

4 → 84

Calls

4 calls:

33.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
26.0ms	(/.f64 x (*.f64 y y))
22.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
2.0ms	(/.f64 1 (*.f64 y y))

rewrite69.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
26×	`distribute-lft-out_binary64`
24×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 146

Calls

4 calls:

38.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
13.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
3.0ms	(/.f64 1 (*.f64 y y))
3.0ms	(/.f64 x (*.f64 y y))

simplify140.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-neg_binary64`
251×	`cancel-sign-sub-inv_binary64`
196×	`associate-/r/_binary64`
171×	`distribute-rgt-neg-in_binary64`
166×	`distribute-rgt-in_binary64`

Counts

230 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	5463
1	643	4334
2	2435	3523
3	4370	3521
4	4967	3521

prune141.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	188	4	192

Error

0.0b

Counts

192 → 4

Alt Table

Status	Error	Program
▶	50.2b	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3))
✓	15.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	29.8b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	23.6b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 6062 to 2813 computations (53.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) y)
✓	0.1b	(*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))
✓	0.1b	(pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3)
✓	27.0b	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3))

series118.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

58.0ms	(pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3)
36.0ms	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3))
18.0ms	(*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))
5.0ms	(/.f64 (+.f64 x -1) y)

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
19×	`associate-l_binary64`

Counts

4 → 142

Calls

4 calls:

16.0ms	(*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))
4.0ms	(/.f64 (+.f64 x -1) y)
3.0ms	(pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3)
3.0ms	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3))

simplify115.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

508×	`associate-+r+_binary64`
450×	`fma-def_binary64`
329×	`associate-+l+_binary64`
191×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Counts

238 → 261

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	433	7203
1	1382	6599
2	5298	6599

prune194.0ms (4.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	261	4	265

Error

0.0b

Counts

265 → 4

Alt Table

Status	Error	Program
✓	50.2b	(cbrt.f64 (pow.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1))) 3))
✓	15.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	29.8b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	23.6b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 8303 to 6083 computations (26.7% saved)

regimes906.0ms (21.7%)

Accuracy

Total 0.1b remaining (71%)

Threshold costs 0.1b (71%)

Counts

88 → 3

Compiler

Compiled 6565 to 4776 computations (27.3% saved)

bsearch29.0ms (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)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

26×	`cancel-sign-sub-inv_binary64`
20×	`+-commutative_binary64`
19×	`sub-neg_binary64`
17×	`neg-sub0_binary64`
17×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	78
1	41	78
2	62	78
3	87	78
4	108	78
5	124	78
6	131	78
7	139	78
8	154	78
9	166	78
10	175	78
11	178	78
12	174	78

end87.0ms (2.1%)

Compiler: Compiled 174 to 109 computations (37.4% saved)

Iter	Nodes	Cost
0	26	78
1	41	78
2	62	78
3	87	78
4	108	78
5	124	78
6	131	78
7	139	78
8	154	78
9	166	78
10	175	78
11	178	78
12	174	78

Iter	Nodes	Cost
0	26	78
1	41	78
2	62	78
3	87	78
4	108	78
5	124	78
6	131	78
7	139	78
8	154	78
9	166	78
10	175	78
11	178	78
12	174	78

Details

analyze145.0ms (3.5%)

sample1.3s (32.1%)

simplify198.0ms (4.7%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series19.0ms (0.5%)

rewrite12.0ms (0.3%)

simplify113.0ms (2.7%)

prune71.0ms (1.7%)

localize6.0ms (0.1%)

series26.0ms (0.6%)

rewrite30.0ms (0.7%)

simplify120.0ms (2.9%)

prune138.0ms (3.3%)

localize11.0ms (0.3%)

series84.0ms (2%)

rewrite69.0ms (1.6%)

simplify140.0ms (3.4%)

prune141.0ms (3.4%)

localize12.0ms (0.3%)

series118.0ms (2.8%)

rewrite34.0ms (0.8%)

simplify115.0ms (2.7%)

prune194.0ms (4.6%)

regimes906.0ms (21.7%)

bsearch29.0ms (0.7%)

simplify8.0ms (0.2%)

end87.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	26	78
1	41	78
2	62	78
3	87	78
4	108	78
5	124	78
6	131	78
7	139	78
8	154	78
9	166	78
10	175	78
11	178	78
12	174	78