Details

analyze103.0ms (3.9%)

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)

sample1.1s (42.2%)

Results

633.0ms	6506×	body	128	valid
180.0ms	614×	body	1024	valid
163.0ms	692×	body	512	valid
71.0ms	441×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify30.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
611×	`fma-neg_binary64`
471×	`div-sub_binary64`
314×	`distribute-rgt-in_binary64`
295×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	111	14
4	326	14
5	893	14
6	2378	14
7	3638	14

Stop Event

1×	node limit

Counts

1 → 2

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

13.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.6b	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
	21.4b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 -1 y))
✓	2.4b	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)

series13.0ms (0.5%)

Counts

2 → 36

Calls

2 calls:

11.0ms	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
2.0ms	(/.f64 y (-.f64 -1 y))

rewrite51.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

443×	`log-prod_binary64`
234×	`prod-diff_binary64`
173×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`
150×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	195	21
2	2600	21

Stop Event

1×	node limit

Counts

2 → 64

Calls

2 calls:

49.0ms	(/.f64 y (-.f64 -1 y))
49.0ms	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)

simplify33.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

547×	`associate-+l-_binary64`
449×	`cancel-sign-sub-inv_binary64`
416×	`fma-neg_binary64`
397×	`sub-neg_binary64`
385×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	624
1	177	613
2	555	587
3	2124	547

Stop Event

1×	node limit

Counts

100 → 98

prune60.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Error

0.0b

Counts

100 → 4

Alt Table

Status	Error	Program
▶	32.5b	(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 x (pow.f64 y 2)) x)) (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))
✓	13.6b	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
	33.0b	(*.f64 (/.f64 x (+.f64 1 y)) y)
	37.8b	(/.f64 (*.f64 y x) (+.f64 1 y))

Compiler

Compiled 1608 to 1151 computations (28.4% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (pow.f64 y 2))
✓	3.3b	(+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2)))
✓	6.1b	(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 x (pow.f64 y 2)) x)) (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))
✓	6.4b	(/.f64 x (pow.f64 y 2))

series74.0ms (2.8%)

Counts

4 → 15

Calls

4 calls:

33.0ms	(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 x (pow.f64 y 2)) x)) (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))
23.0ms	(/.f64 x (pow.f64 y 2))
17.0ms	(+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2)))
2.0ms	(/.f64 1 (pow.f64 y 2))

rewrite52.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`
169×	`add-sqr-sqrt_binary64`
167×	`add-cbrt-cube_binary64`
159×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	347	47

Stop Event

1×	node limit

Counts

4 → 156

Calls

4 calls:

49.0ms	(/.f64 1 (pow.f64 y 2))
49.0ms	(+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2)))
49.0ms	(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 x (pow.f64 y 2)) x)) (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))
49.0ms	(/.f64 x (pow.f64 y 2))

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
352×	`fma-neg_binary64`
251×	`distribute-neg-frac_binary64`
224×	`times-frac_binary64`
168×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	147
1	64	141
2	162	132
3	454	126
4	1299	126
5	4065	126

Stop Event

1×	node limit

Counts

171 → 171

prune134.0ms (5.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	170	5	175

Error

Counts

175 → 5

Alt Table

Status	Error	Program
✓	32.5b	(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 x (pow.f64 y 2)) x)) (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))
✓	13.6b	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
	34.2b	(fma.f64 (cbrt.f64 (pow.f64 y -2)) (cbrt.f64 (pow.f64 y -1)) (-.f64 (fma.f64 x (pow.f64 y -2) x) (+.f64 (/.f64 x y) (pow.f64 y -2))))
▶	33.0b	(*.f64 (/.f64 x (+.f64 1 y)) y)
	37.8b	(/.f64 (*.f64 y x) (+.f64 1 y))

Compiler

Compiled 5226 to 3150 computations (39.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 1 y))
✓	6.3b	(*.f64 (/.f64 x (+.f64 1 y)) y)

series18.0ms (0.7%)

Counts

2 → 36

Calls

2 calls:

10.0ms	(*.f64 (/.f64 x (+.f64 1 y)) y)
8.0ms	(/.f64 x (+.f64 1 y))

rewrite46.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`log1p-expm1-u_binary64`
776×	`expm1-log1p-u_binary64`
96×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
69×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	150	17
2	2041	17

Stop Event

1×	node limit

Counts

2 → 60

Calls

2 calls:

45.0ms	(/.f64 x (+.f64 1 y))
45.0ms	(*.f64 (/.f64 x (+.f64 1 y)) y)

simplify41.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

714×	`times-frac_binary64`
636×	`fma-def_binary64`
363×	`cancel-sign-sub-inv_binary64`
321×	`fma-neg_binary64`
263×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	458
1	125	447
2	378	439
3	1212	436
4	4681	436

Stop Event

1×	node limit

Counts

96 → 88

prune45.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Error

Counts

93 → 5

Alt Table

Status	Error	Program
✓	32.5b	(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 x (pow.f64 y 2)) x)) (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))
✓	13.6b	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
	34.2b	(fma.f64 (cbrt.f64 (pow.f64 y -2)) (cbrt.f64 (pow.f64 y -1)) (-.f64 (fma.f64 x (pow.f64 y -2) x) (+.f64 (/.f64 x y) (pow.f64 y -2))))
▶	30.1b	(/.f64 x (/.f64 (+.f64 1 y) y))
✓	33.0b	(*.f64 (/.f64 x (+.f64 1 y)) y)

Compiler

Compiled 1116 to 634 computations (43.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 y) y)
✓	0.1b	(/.f64 x (/.f64 (+.f64 1 y) y))

series11.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

10.0ms	(/.f64 x (/.f64 (+.f64 1 y) y))
2.0ms	(/.f64 (+.f64 1 y) y)

rewrite45.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

867×	`log1p-expm1-u_binary64`
867×	`expm1-log1p-u_binary64`
123×	`prod-diff_binary64`
78×	`add-sqr-sqrt_binary64`
76×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	17
2	2280	17

Stop Event

1×	node limit

Counts

2 → 76

Calls

2 calls:

43.0ms	(/.f64 (+.f64 1 y) y)
43.0ms	(/.f64 x (/.f64 (+.f64 1 y) y))

simplify33.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

415×	`fma-def_binary64`
287×	`distribute-rgt-neg-in_binary64`
255×	`distribute-lft-neg-in_binary64`
253×	`fma-neg_binary64`
248×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	345
1	90	337
2	250	332
3	786	332
4	3304	332

Stop Event

1×	node limit

Counts

112 → 95

prune48.0ms (1.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	95	5	100

Error

Counts

100 → 5

Alt Table

Status	Error	Program
✓	32.5b	(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 x (pow.f64 y 2)) x)) (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))
✓	13.6b	(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
	34.2b	(fma.f64 (cbrt.f64 (pow.f64 y -2)) (cbrt.f64 (pow.f64 y -1)) (-.f64 (fma.f64 x (pow.f64 y -2) x) (+.f64 (/.f64 x y) (pow.f64 y -2))))
✓	30.1b	(/.f64 x (/.f64 (+.f64 1 y) y))
✓	33.0b	(*.f64 (/.f64 x (+.f64 1 y)) y)

Compiler

Compiled 1171 to 718 computations (38.7% saved)

regimes472.0ms (18.1%)

Accuracy

Total 0.0b remaining (22.3%)

Threshold costs 0.0b (22.3%)

Counts

52 → 3

Compiler

Compiled 4095 to 2814 computations (31.3% saved)

bsearch31.0ms (1.2%)

Steps

Iters	Range		Point
8	205074.01309889826	346370982.3723807	296276.6823099669
8	-2111244066.0090704	-2172304.324295389	-2212979.2993776714

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	94
1	41	94
2	54	94
3	68	94
4	78	94
5	83	94
6	84	94

Stop Event

1×

saturated

end100.0ms (3.8%)

Compiler: Compiled 208 to 140 computations (32.7% saved)

Details

analyze103.0ms (3.9%)

sample1.1s (42.2%)

simplify30.0ms (1.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series13.0ms (0.5%)

rewrite51.0ms (1.9%)

simplify33.0ms (1.3%)

prune60.0ms (2.3%)

localize12.0ms (0.4%)

series74.0ms (2.8%)

rewrite52.0ms (2%)

simplify35.0ms (1.3%)

prune134.0ms (5.1%)

localize4.0ms (0.2%)

series18.0ms (0.7%)

rewrite46.0ms (1.8%)

simplify41.0ms (1.6%)

prune45.0ms (1.7%)

localize4.0ms (0.2%)

series11.0ms (0.4%)

rewrite45.0ms (1.7%)

simplify33.0ms (1.3%)

prune48.0ms (1.8%)

regimes472.0ms (18.1%)

bsearch31.0ms (1.2%)

simplify5.0ms (0.2%)

end100.0ms (3.8%)

Profiling