Details

analyze10.0ms (0.4%)

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)

sample1.1s (41.6%)

Results

956.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify113.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1572×	`fma-neg_binary64`
1419×	`fma-def_binary64`
565×	`sub-neg_binary64`
397×	`div-sub_binary64`
395×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	31	19
2	50	19
3	71	19
4	84	19
5	103	19
6	137	19
7	208	19
8	304	19
9	493	19
10	931	19
11	1441	19
12	2503	19
13	3175	19
14	3604	19
15	4118	19
16	4302	19
17	4751	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 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize9.0ms (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))

series10.0ms (0.4%)

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)

rewrite71.0ms (2.7%)

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:

66.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
66.0ms	(fma.f64 x 4481/100000 99229/100000)
66.0ms	(fma.f64 x 27061/100000 230753/100000)
66.0ms	(/.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

simplify93.0ms (3.6%)

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

prune255.0ms (9.8%)

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 (fma.f64 x -20191289437/10000000000 230753/100000) x)
▶	0.0b	(-.f64 (*.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)))) x)

Status

Error

Program

25.5b

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

▶

0.0b

(-.f64 (*.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)))) x)

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))

series21.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

12.0ms

(/.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))))

rewrite85.0ms (3.2%)

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:

81.0ms

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

81.0ms

(*.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))))

81.0ms

(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

simplify63.0ms (2.4%)

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

prune299.0ms (11.5%)

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 (fma.f64 x -20191289437/10000000000 230753/100000) x)
✓	0.0b	(-.f64 (*.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)))) x)

Status

Error

Program

▶

25.5b

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

✓

0.0b

(-.f64 (*.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)))) x)

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 (fma.f64 x -20191289437/10000000000 230753/100000) x)
✓	0.4b	(fma.f64 x -20191289437/10000000000 230753/100000)

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 x -20191289437/10000000000 230753/100000)
2.0ms	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)

rewrite47.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

661×	`log1p-expm1-u_binary64`
661×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
120×	`expm1-udef_binary64`
120×	`log1p-udef_binary64`

Counts

2 → 74

Calls

2 calls:

45.0ms	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)
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	1613	13
3	4975	13
0	0	0
1	0	0

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

30×	`fma-def_binary64`
19×	`sub-neg_binary64`
10×	`+-commutative_binary64`
9×	`*-commutative_binary64`
8×	`fma-neg_binary64`

Counts

98 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	144
1	25	144
2	36	108
3	59	108
4	80	108
5	111	108
6	132	108
7	145	108
8	155	108
9	124	108

prune47.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	83	2	85

Error

Counts

85 → 2

Alt Table

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

Status

Error

Program

✓

25.5b

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

✓

0.0b

(-.f64 (*.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)))) x)

Compiler

Compiled 1076 to 738 computations (31.4% saved)

regimes296.0ms (11.3%)

Accuracy

Total 0.0b remaining (13.5%)

Threshold costs 0.0b (13.5%)

Counts

150 → 1

Compiler

Compiled 5614 to 4358 computations (22.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	16	22
2	21	22
3	23	22
4	24	22
5	24	22

end65.0ms (2.5%)

Compiler: Compiled 66 to 50 computations (24.2% saved)

Iter	Nodes	Cost
0	13	144
1	25	144
2	36	108
3	59	108
4	80	108
5	111	108
6	132	108
7	145	108
8	155	108
9	124	108

Iter	Nodes	Cost
0	13	144
1	25	144
2	36	108
3	59	108
4	80	108
5	111	108
6	132	108
7	145	108
8	155	108
9	124	108

Details

analyze10.0ms (0.4%)

sample1.1s (41.6%)

simplify113.0ms (4.3%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series10.0ms (0.4%)

rewrite71.0ms (2.7%)

simplify93.0ms (3.6%)

prune255.0ms (9.8%)

localize11.0ms (0.4%)

series21.0ms (0.8%)

rewrite85.0ms (3.2%)

simplify63.0ms (2.4%)

prune299.0ms (11.5%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite47.0ms (1.8%)

simplify17.0ms (0.6%)

prune47.0ms (1.8%)

regimes296.0ms (11.3%)

simplify3.0ms (0.1%)

end65.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	13	144
1	25	144
2	36	108
3	59	108
4	80	108
5	111	108
6	132	108
7	145	108
8	155	108
9	124	108