Details

analyze8.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	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%	0%	14

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample1.0s (40.8%)

Results

918.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify108.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1041×	`fma-neg_binary64`
807×	`times-frac_binary64`
600×	`associate-/r/_binary64`
564×	`sub-neg_binary64`
392×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	25	19
2	45	19
3	72	19
4	115	19
5	188	19
6	308	19
7	491	19
8	989	19
9	1283	19
10	3056	19
11	4408	19
12	4532	19
13	4794	19
14	4959	19
15	4564	19

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	14.3b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series8.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
2.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
1.0ms	(fma.f64 x 27061/100000 230753/100000)
1.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite73.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

509×	`unpow-prod-down_binary64`
418×	`log-prod_binary64`
268×	`pow2_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

4 → 165

Calls

4 calls:

70.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
70.0ms	(fma.f64 x 4481/100000 99229/100000)
70.0ms	(fma.f64 x 27061/100000 230753/100000)
70.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	225	35
2	2451	35
3	5654	35
0	0	0
1	0	0

simplify97.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
739×	`cancel-sign-sub-inv_binary64`
417×	`times-frac_binary64`
305×	`fma-def_binary64`
239×	`neg-mul-1_binary64`

Counts

213 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	459
1	130	417
2	295	389
3	716	369
4	2068	369
5	4656	369
6	4991	369
7	4998	369
8	4919	369

prune215.0ms (8.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	2	198

Error

Counts

198 → 2

Alt Table

Status	Error	Program
	25.5b	(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))
▶	0.0b	(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Status

Error

Program

25.5b

(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))

▶

0.0b

(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 4259 to 3313 computations (22.2% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	14.2b	(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series19.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

10.0ms

(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

6.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

3.0ms

(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

rewrite78.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

592×	`log-prod_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
202×	`log-pow_binary64`
137×	`add-sqr-sqrt_binary64`

Counts

3 → 133

Calls

3 calls:

75.0ms

(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

75.0ms

(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

75.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	292	45
2	3276	45
3	5460	45
0	0	0
1	0	0

simplify69.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-neg_binary64`
425×	`fma-def_binary64`
369×	`associate--r+_binary64`
351×	`associate-/r*_binary64`
338×	`associate--l+_binary64`

Counts

169 → 191

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	921
1	445	883
2	1449	853
3	4681	844
4	5361	844

prune314.0ms (12.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	284	2	286

Error

Counts

286 → 2

Alt Table

Status	Error	Program
▶	25.5b	(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))
✓	0.0b	(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Status

Error

Program

▶

25.5b

(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))

✓

0.0b

(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 8958 to 7146 computations (20.2% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))
✓	0.4b	(fma.f64 x -20191289437/10000000000 230753/100000)

series3.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))
2.0ms	(fma.f64 x -20191289437/10000000000 230753/100000)

rewrite47.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
394×	`prod-diff_binary64`
120×	`log1p-udef_binary64`
72×	`egg-rr`

Counts

2 → 72

Calls

2 calls:

45.0ms	(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))
45.0ms	(fma.f64 x -20191289437/10000000000 230753/100000)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	134	13
2	1621	13
3	4924	13
0	0	0
1	0	0

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
12×	`sub-neg_binary64`
7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`fma-neg_binary64`

Counts

96 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	126
1	22	126
2	31	108
3	44	108
4	55	108
5	72	108
6	87	108
7	96	108
8	106	108
9	110	108
10	111	108
11	85	108

prune51.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	82	2	84

Error

Counts

84 → 2

Alt Table

Status	Error	Program
✓	25.5b	(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))
✓	0.0b	(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Status

Error

Program

✓

25.5b

(-.f64 x (fma.f64 x -20191289437/10000000000 230753/100000))

✓

0.0b

(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 1160 to 861 computations (25.8% saved)

regimes319.0ms (12.5%)

Accuracy

Total -0.0b remaining (-183.9%)

Threshold costs -0.0b (-183.9%)

Counts

151 → 1

Compiler

Compiled 5674 to 4406 computations (22.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	18	19
2	24	19
3	28	19
4	31	19
5	32	19
6	31	19

end63.0ms (2.4%)

Compiler: Compiled 64 to 48 computations (25% saved)

Iter	Nodes	Cost
0	12	126
1	22	126
2	31	108
3	44	108
4	55	108
5	72	108
6	87	108
7	96	108
8	106	108
9	110	108
10	111	108
11	85	108

Iter	Nodes	Cost
0	12	126
1	22	126
2	31	108
3	44	108
4	55	108
5	72	108
6	87	108
7	96	108
8	106	108
9	110	108
10	111	108
11	85	108

Details

analyze8.0ms (0.3%)

sample1.0s (40.8%)

simplify108.0ms (4.2%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite73.0ms (2.8%)

simplify97.0ms (3.8%)

prune215.0ms (8.4%)

localize11.0ms (0.4%)

series19.0ms (0.7%)

rewrite78.0ms (3.1%)

simplify69.0ms (2.7%)

prune314.0ms (12.3%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite47.0ms (1.8%)

simplify16.0ms (0.6%)

prune51.0ms (2%)

regimes319.0ms (12.5%)

simplify3.0ms (0.1%)

end63.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	12	126
1	22	126
2	31	108
3	44	108
4	55	108
5	72	108
6	87	108
7	96	108
8	106	108
9	110	108
10	111	108
11	85	108