Details

analyze62.0ms (2.2%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample985.0ms (35.3%)

Results

886.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify75.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
382×	`times-frac_binary64`
357×	`div-sub_binary64`
168×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	28	10
5	51	10
6	74	10
7	104	10
8	154	10
9	319	10
10	479	10
11	806	10
12	1050	10
13	1216	10
14	1316	10
15	1330	10
16	1350	10
17	1350	10
18	1250	10

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite53.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
552×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
69×	`add-log-exp_binary64`

Counts

1 → 35

Calls

1 calls:

52.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	140	10
2	2045	10
3	6174	10
0	0	0
1	0	0

simplify47.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

825×	`associate-/l*_binary64`
574×	`fma-neg_binary64`
505×	`associate-/r*_binary64`
368×	`associate-/r/_binary64`
338×	`cancel-sign-sub-inv_binary64`

Counts

59 → 49

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	417
1	119	399
2	366	339
3	1394	327
4	4483	318
5	4972	318

prune33.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.0b

Counts

50 → 3

Alt Table

Status	Error	Program
▶	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)
	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) 1)
	32.5b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)

Compiler

Compiled 715 to 301 computations (57.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series23.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)
11.0ms	(/.f64 (-.f64 x y) (+.f64 x y))

rewrite123.0ms (4.4%)

Algorithm

2×	batch-egg-rewrite

Rules

768×	`prod-diff_binary64`
630×	`fma-udef_binary64`
250×	`fma-def_binary64`
218×	`fma-neg_binary64`
167×	`expm1-udef_binary64`

Counts

2 → 114

Calls

2 calls:

120.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)
120.0ms	(/.f64 (-.f64 x y) (+.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	185	20
2	2568	20
3	4816	20
4	4665	20
5	4933	20
0	0	0
1	0	0

simplify64.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

757×	`cancel-sign-sub-inv_binary64`
496×	`fma-neg_binary64`
412×	`associate-/r/_binary64`
247×	`neg-mul-1_binary64`
239×	`neg-sub0_binary64`

Counts

162 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	831
1	159	807
2	496	705
3	1827	666
4	4543	666
5	5019	666

prune96.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	139	4	143

Error

Counts

143 → 4

Alt Table

Status	Error	Program
▶	0.0b	(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3) -1)
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)
	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) 1)
	32.5b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)

Compiler

Compiled 2742 to 1008 computations (63.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3) -1)
✓	0.0b	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
✓	0.0b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3)

series139.0ms (5%)

Counts

3 → 72

Calls

3 calls:

64.0ms	(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3) -1)
50.0ms	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3)
25.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))

rewrite164.0ms (5.9%)

Algorithm

2×	batch-egg-rewrite

Rules

768×	`prod-diff_binary64`
337×	`egg-rr`
196×	`log1p-udef_binary64`
195×	`expm1-udef_binary64`
113×	`add-sqr-sqrt_binary64`

Counts

3 → 337

Calls

3 calls:

150.0ms	(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3) -1)
150.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
150.0ms	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	235	32
2	3033	32
3	4997	32
4	5102	32
0	0	0
1	0	0

simplify91.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

748×	`fma-neg_binary64`
722×	`fma-def_binary64`
549×	`times-frac_binary64`
366×	`associate-/l*_binary64`
343×	`cancel-sign-sub-inv_binary64`

Counts

409 → 398

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1764
1	363	1647
2	1405	1430
3	4860	1427
4	5401	1427

prune309.0ms (11.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	480	0	480
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	480	4	484

Error

Counts

484 → 4

Alt Table

Status	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3) -1)
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)
▶	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) 1)
	32.5b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)

Compiler

Compiled 17313 to 5343 computations (69.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) 1)
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.1b	(exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
✓	2.3b	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

series58.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
21.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) 1)
15.0ms	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

rewrite68.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

851×	`prod-diff_binary64`
179×	`log1p-udef_binary64`
178×	`expm1-udef_binary64`
111×	`egg-rr`
101×	`add-sqr-sqrt_binary64`

Counts

3 → 111

Calls

3 calls:

66.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) 1)
66.0ms	(exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
66.0ms	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	201	35
2	2716	35
3	4964	35
0	0	0
1	0	0

simplify80.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-+l+_binary64`
561×	`times-frac_binary64`
464×	`fma-def_binary64`
397×	`associate-/l*_binary64`
337×	`fma-neg_binary64`

Counts

183 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2271
1	370	1674
2	1169	1449
3	4322	1440
4	4966	1440

prune144.0ms (5.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	229	4	233

Error

Counts

233 → 4

Alt Table

Status	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) 3) -1)
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)
✓	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))) 1)
	32.5b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)

Compiler

Compiled 4500 to 2398 computations (46.7% saved)

regimes78.0ms (2.8%)

Accuracy

Total 0.0b remaining (61.2%)

Threshold costs 0.0b (61.2%)

Counts

30 → 1

Compiler

Compiled 1070 to 788 computations (26.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13
2	15	13
3	17	13
4	18	13
5	18	13

end60.0ms (2.2%)

Compiler: Compiled 74 to 49 computations (33.8% saved)

Details

analyze62.0ms (2.2%)

sample985.0ms (35.3%)

simplify75.0ms (2.7%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite53.0ms (1.9%)

simplify47.0ms (1.7%)

prune33.0ms (1.2%)

localize5.0ms (0.2%)

series23.0ms (0.8%)

rewrite123.0ms (4.4%)

simplify64.0ms (2.3%)

prune96.0ms (3.4%)

localize7.0ms (0.3%)

series139.0ms (5%)

rewrite164.0ms (5.9%)

simplify91.0ms (3.3%)

prune309.0ms (11.1%)

localize8.0ms (0.3%)

series58.0ms (2.1%)

rewrite68.0ms (2.4%)

simplify80.0ms (2.9%)

prune144.0ms (5.2%)

regimes78.0ms (2.8%)

simplify2.0ms (0.1%)

end60.0ms (2.2%)

Profiling