Details

analyze9.0ms (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
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.6s (34.8%)

Results

515.0ms	1379×	body	1024	valid
478.0ms	4524×	body	128	valid
450.0ms	1611×	body	512	valid
138.0ms	742×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify17.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

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

8.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	1.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series13.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite218.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

757×	`*-un-lft-identity_binary64`
733×	`times-frac_binary64`
558×	`add-sqr-sqrt_binary64`
508×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

4 → 668

Calls

4 calls:

75.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
19.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(/.f64 1 (-.f64 x 1))

simplify411.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
457×	`times-frac_binary64`
236×	`fma-def_binary64`
186×	`sub-neg_binary64`
176×	`exp-prod_binary64`

Counts

716 → 853

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	19278
1	989	13709
2	2519	9843
3	4349	9843
4	4815	9843

prune796.0ms (17.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	850	4	854

Error

0.2b

Counts

854 → 4

Alt Table

Status	Error	Program
✓	8.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	25.4b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))
	30.3b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
	33.3b	(fma.f64 -2 x (/.f64 -2 x))

Compiler

Compiled 33623 to 26163 computations (22.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
	0.0b	(/.f64 1 (-.f64 x 1))
	1.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	1.3b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))

series8.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-def_binary64`
452×	`fma-neg_binary64`
402×	`neg-mul-1_binary64`
281×	`times-frac_binary64`
280×	`cancel-sign-sub-inv_binary64`

Counts

23 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	537
1	152	486
2	424	480
3	1205	480
4	3448	480
5	4191	480
6	5081	480

prune752.0ms (16.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	832	1	833
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	834	3	837

Error

0.2b

Counts

837 → 3

Alt Table

Status	Error	Program
✓	8.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	33.8b	(*.f64 -2 (+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x x 1) (pow.f64 x 5))))
▶	30.3b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))

Compiler

Compiled 34784 to 27420 computations (21.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 2 (pow.f64 x 5))
✓	0.2b	(/.f64 2 (pow.f64 x 3))

series6.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

3.0ms	(/.f64 2 (pow.f64 x 5))
3.0ms	(/.f64 2 (pow.f64 x 3))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`

Counts

2 → 114

Calls

2 calls:

4.0ms	(/.f64 2 (pow.f64 x 3))
3.0ms	(/.f64 2 (pow.f64 x 5))

simplify113.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

767×	`associate-/r*_binary64`
450×	`times-frac_binary64`
425×	`associate-l_binary64`
377×	`log-prod_binary64`
336×	`fma-def_binary64`

Counts

114 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	1600
1	257	1540
2	807	1540
3	3985	1484
4	4413	1428
5	4998	1428
6	5081	1428

prune104.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	125	5	130

Error

Counts

130 → 5

Alt Table

Status	Error	Program
	46.8b	(+.f64 (/.f64 (/.f64 2 (pow.f64 x 3/2)) (pow.f64 (sqrt.f64 x) 3)) (/.f64 2 (pow.f64 x 5)))
	33.8b	(*.f64 -2 (+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x x 1) (pow.f64 x 5))))
✓	8.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	30.2b	(+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 5)))
✓	30.3b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))

Compiler

Compiled 2454 to 1996 computations (18.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 2 (pow.f64 x 5))
✓	0.1b	(/.f64 (/.f64 2 x) (*.f64 x x))

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(/.f64 (/.f64 2 x) (*.f64 x x))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 48

Calls

1 calls:

5.0ms

(/.f64 (/.f64 2 x) (*.f64 x x))

simplify127.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

586×	`div-sub_binary64`
337×	`*-commutative_binary64`
333×	`sub-neg_binary64`
305×	`associate-/l/_binary64`
305×	`times-frac_binary64`

Counts

60 → 76

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	105	779
1	227	689
2	591	689
3	1852	689
4	2243	674
5	2845	674
6	3851	647
7	4175	647
8	4804	647
9	4921	647
10	4607	647

prune84.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
✓	8.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	30.2b	(+.f64 (/.f64 (/.f64 (/.f64 2 x) x) x) (/.f64 2 (pow.f64 x 5)))
	33.8b	(*.f64 -2 (+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x x 1) (pow.f64 x 5))))
✓	30.3b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))

Compiler

Compiled 2769 to 1908 computations (31.1% saved)

regimes122.0ms (2.6%)

Accuracy

Total 0.5b remaining (88.9%)

Threshold costs 0.5b (88.9%)

Counts

36 → 3

Compiler

Compiled 1296 to 1044 computations (19.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	116
1	42	116
2	48	116
3	50	116
4	51	116
5	48	116

end94.0ms (2%)

Compiler: Compiled 218 to 168 computations (22.9% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze9.0ms (0.2%)

sample1.6s (34.8%)

simplify17.0ms (0.4%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

series13.0ms (0.3%)

rewrite218.0ms (4.7%)

simplify411.0ms (8.9%)

prune796.0ms (17.2%)

localize11.0ms (0.2%)

series8.0ms (0.2%)

rewrite1.0ms (0%)

simplify83.0ms (1.8%)

prune752.0ms (16.2%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite12.0ms (0.3%)

simplify113.0ms (2.4%)

prune104.0ms (2.2%)

localize7.0ms (0.2%)

series6.0ms (0.1%)

rewrite8.0ms (0.2%)

simplify127.0ms (2.7%)

prune84.0ms (1.8%)

regimes122.0ms (2.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end94.0ms (2%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22