Details

analyze440.0ms (12.2%)

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
12.5%	87.4%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.1%	0.1%	7
35.9%	64%	0.1%	8
47.2%	52.7%	0.1%	9
52.1%	47.8%	0.1%	10
65.3%	34.5%	0.1%	11
71.4%	28.4%	0.1%	12
74.2%	25.6%	0.1%	13
81.7%	18.1%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.0s (28.6%)

Results

894.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify149.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

2495×	`fma-neg_binary64`
1241×	`fma-def_binary64`
1051×	`div-sub_binary64`
520×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	31	18
3	48	18
4	71	18
5	103	18
6	155	18
7	209	18
8	270	18
9	300	16
10	389	16
11	599	16
12	934	16
13	1583	16
14	1525	16
15	1839	16
16	1745	16
17	1773	16
18	1933	16
19	2758	16
20	3102	16
21	4012	16
22	4885	16
23	4851	16

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	3.7b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.1b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.2b	(/.f64 -5641895835477563/5000000000000000 y)

series101.0ms (2.8%)

Counts

4 → 108

Calls

4 calls:

44.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
42.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
13.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
1.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite125.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

675×	`prod-diff_binary64`
487×	`fma-udef_binary64`
256×	`fma-def_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`

Counts

4 → 111

Calls

4 calls:

123.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
123.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
123.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
123.0ms	(/.f64 -5641895835477563/5000000000000000 y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	234	43
2	2881	43
3	4890	43
4	4781	43
5	4923	43
0	0	0
1	0	0

simplify78.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

711×	`associate-/l*_binary64`
623×	`associate-/r*_binary64`
481×	`fma-def_binary64`
150×	`distribute-rgt-in_binary64`
135×	`distribute-neg-in_binary64`

Counts

219 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	2745
1	436	2727
2	1581	2570
3	5204	2570

prune121.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	173	3	176

Error

0.0b

Counts

176 → 3

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	23.0b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
▶	3.7b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3888 to 2431 computations (37.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	1.4b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	10.7b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series85.0ms (2.4%)

Counts

4 → 112

Calls

4 calls:

38.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
36.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
9.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
2.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite91.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

567×	`fma-def_binary64`
275×	`fma-neg_binary64`
242×	`egg-rr`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`

Counts

4 → 242

Calls

4 calls:

85.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
85.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
85.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
85.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	248	51
2	3364	51
3	4999	51
0	0	0
1	0	0

simplify106.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

636×	`associate-/l*_binary64`
572×	`fma-def_binary64`
527×	`associate-/r*_binary64`
199×	`fma-neg_binary64`
196×	`associate-*l/_binary64`

Counts

354 → 312

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	2764
1	422	2744
2	1493	2629
3	4889	2621
4	4988	2621

prune211.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	311	4	315

Error

Counts

315 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	23.0b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	3.7b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
▶	3.9b	(fma.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 y x))) x)

Compiler

Compiled 7552 to 3533 computations (53.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.7b	(/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 y x)))
✓	1.4b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 y x))
✓	2.0b	(fma.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 y x))) x)

series88.0ms (2.4%)

Counts

3 → 74

Calls

3 calls:

42.0ms

(fma.f64 y (/.f64 1 (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 y x))) x)

36.0ms

(/.f64 1 (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 y x)))

9.0ms

(-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 y x))

rewrite91.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

600×	`log-prod_binary64`
413×	`fma-def_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
220×	`egg-rr`

Counts

3 → 220

Calls

3 calls:

85.0ms

(/.f64 1 (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 y x)))

85.0ms

(-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 y x))

85.0ms

(fma.f64 y (/.f64 1 (-.f64 (*.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 y x))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	253	45
2	3042	45
3	5720	45
0	0	0
1	0	0

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

868×	`associate-/r*_binary64`
780×	`fma-def_binary64`
236×	`associate-/r/_binary64`
177×	`cancel-sign-sub-inv_binary64`
165×	`times-frac_binary64`

Counts

294 → 281

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2312
1	550	2282
2	2088	2201
3	5667	2201

prune213.0ms (5.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	301	4	305

Error

Counts

305 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	23.0b	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)
✓	3.7b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	3.9b	(fma.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 y x))) x)

Compiler

Compiled 7405 to 3629 computations (51% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 5000000000000000/5641895835477563 (exp.f64 z))
✓	0.1b	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)

series24.0ms (0.7%)

Counts

2 → 40

Calls

2 calls:

18.0ms	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)
6.0ms	(/.f64 5000000000000000/5641895835477563 (exp.f64 z))

rewrite82.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

706×	`log1p-expm1-u_binary64`
706×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
84×	`prod-diff_binary64`

Counts

2 → 45

Calls

2 calls:

81.0ms	(/.f64 5000000000000000/5641895835477563 (exp.f64 z))
81.0ms	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	162	16
2	1864	16
3	4966	16
4	4916	16
0	0	0
1	0	0

simplify97.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
544×	`cancel-sign-sub-inv_binary64`
534×	`distribute-rgt-neg-in_binary64`
440×	`distribute-lft-neg-in_binary64`
418×	`associate-l_binary64`

Counts

85 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	414
1	110	410
2	300	395
3	900	372
4	2996	372
5	4707	372
6	4988	372
7	4945	372

prune40.0ms (1.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	64	4	68

Error

Counts

68 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	23.0b	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)
✓	3.7b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	3.9b	(fma.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 y x))) x)

Compiler

Compiled 777 to 468 computations (39.8% saved)

regimes220.0ms (6.1%)

Accuracy

Total 0.2b remaining (98.6%)

Threshold costs 0.2b (98.6%)

Counts

44 → 3

Compiler

Compiled 3483 to 2491 computations (28.5% saved)

bsearch26.0ms (0.7%)

Steps

Iters	Range		Point
0	1.1283791670955126	1.128379167095637	1.1283791670955747
13	0.0	1.1283785090324137	2.50107737796091e-308

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	59
1	36	59
2	50	59
3	58	59
4	63	59
5	64	59
6	62	59

end77.0ms (2.1%)

Compiler: Compiled 139 to 92 computations (33.8% saved)

Details

analyze440.0ms (12.2%)

sample1.0s (28.6%)

simplify149.0ms (4.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series101.0ms (2.8%)

rewrite125.0ms (3.5%)

simplify78.0ms (2.2%)

prune121.0ms (3.3%)

localize8.0ms (0.2%)

series85.0ms (2.4%)

rewrite91.0ms (2.5%)

simplify106.0ms (2.9%)

prune211.0ms (5.9%)

localize8.0ms (0.2%)

series88.0ms (2.4%)

rewrite91.0ms (2.5%)

simplify75.0ms (2.1%)

prune213.0ms (5.9%)

localize5.0ms (0.1%)

series24.0ms (0.7%)

rewrite82.0ms (2.3%)

simplify97.0ms (2.7%)

prune40.0ms (1.1%)

regimes220.0ms (6.1%)

bsearch26.0ms (0.7%)

simplify5.0ms (0.1%)

end77.0ms (2.1%)

Profiling