Details

analyze52.0ms (1.6%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample852.0ms (26.3%)

Results

801.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify28.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1142×	`fma-neg_binary64`
494×	`div-sub_binary64`
253×	`associate-/r/_binary64`
248×	`times-frac_binary64`
239×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	35	13
3	77	13
4	188	13
5	358	13
6	883	13
7	2287	13
8	4591	13

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 42 to 26 computations (38.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series14.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

14.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite117.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

843×	`prod-diff_binary64`
233×	`egg-rr`
189×	`log1p-udef_binary64`
103×	`add-sqr-sqrt_binary64`
100×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	197	13
2	3058	13

Stop Event

1×	node limit

Counts

1 → 233

Calls

1 calls:

107.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

simplify35.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
491×	`times-frac_binary64`
377×	`associate-/l*_binary64`
339×	`associate-/r*_binary64`
210×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1038
1	418	1030
2	1608	918

Stop Event

1×	node limit

Counts

257 → 262

prune285.0ms (8.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	259	4	263

Error

Counts

263 → 4

Alt Table

Status	Error	Program
	0.5b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2))
▶	0.0b	(-.f64 (/.f64 x (-.f64 (-.f64 2 y) x)) (/.f64 y (-.f64 (-.f64 2 y) x)))
	42.0b	(fma.f64 (/.f64 x y) -2 (+.f64 1 (/.f64 2 y)))
	38.8b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

Compiler

Compiled 15351 to 9950 computations (35.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 (-.f64 2 y) x))
✓	0.0b	(/.f64 y (-.f64 (-.f64 2 y) x))
✓	0.0b	(-.f64 (/.f64 x (-.f64 (-.f64 2 y) x)) (/.f64 y (-.f64 (-.f64 2 y) x)))

series38.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

14.0ms	(-.f64 (/.f64 x (-.f64 (-.f64 2 y) x)) (/.f64 y (-.f64 (-.f64 2 y) x)))
13.0ms	(/.f64 x (-.f64 (-.f64 2 y) x))
11.0ms	(/.f64 y (-.f64 (-.f64 2 y) x))

rewrite83.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

613×	`fma-def_binary64`
331×	`fma-neg_binary64`
227×	`egg-rr`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	229	33
2	3815	33

Stop Event

1×	node limit

Counts

3 → 227

Calls

3 calls:

75.0ms	(/.f64 x (-.f64 (-.f64 2 y) x))
75.0ms	(/.f64 y (-.f64 (-.f64 2 y) x))
75.0ms	(-.f64 (/.f64 x (-.f64 (-.f64 2 y) x)) (/.f64 y (-.f64 (-.f64 2 y) x)))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
394×	`sub-neg_binary64`
331×	`cancel-sign-sub-inv_binary64`
226×	`associate-+r+_binary64`
214×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	2940
1	770	2912
2	3027	2846

Stop Event

1×	node limit

Counts

299 → 310

prune266.0ms (8.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	310	4	314

Error

Counts

314 → 4

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2))
✓	0.0b	(-.f64 (/.f64 x (-.f64 (-.f64 2 y) x)) (/.f64 y (-.f64 (-.f64 2 y) x)))
	42.0b	(fma.f64 (/.f64 x y) -2 (+.f64 1 (/.f64 2 y)))
	38.8b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

Compiler

Compiled 9364 to 5359 computations (42.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))
✓	0.1b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2))
✓	0.2b	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2)
✓	0.2b	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x)))

series403.0ms (12.4%)

Counts

4 → 96

Calls

4 calls:

234.0ms	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2)
138.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x)))
16.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2))
13.0ms	(/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))

rewrite69.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

420×	`fma-def_binary64`
228×	`fma-neg_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
162×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	59
1	263	59
2	3659	59

Stop Event

1×	node limit

Counts

4 → 162

Calls

4 calls:

66.0ms	(/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))
66.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2))
65.0ms	(pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2)
65.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x)))

simplify108.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

371×	`times-frac_binary64`
279×	`*-commutative_binary64`
261×	`associate-/l*_binary64`
230×	`+-commutative_binary64`
220×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	868	8720
1	2945	8581

Stop Event

1×	node limit

Counts

258 → 229

prune420.0ms (12.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	320	4	324

Error

Counts

324 → 4

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2))
✓	0.0b	(-.f64 (/.f64 x (-.f64 (-.f64 2 y) x)) (/.f64 y (-.f64 (-.f64 2 y) x)))
	42.0b	(fma.f64 (/.f64 x y) -2 (+.f64 1 (/.f64 2 y)))
▶	38.8b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

Compiler

Compiled 19450 to 13923 computations (28.4% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

series8.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

rewrite45.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`prod-diff_binary64`
228×	`fma-def_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
129×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	216	14
2	2765	14

Stop Event

1×	node limit

Counts

1 → 50

Calls

1 calls:

44.0ms

(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
624×	`fma-def_binary64`
280×	`cancel-sign-sub-inv_binary64`
106×	`distribute-rgt-in_binary64`
84×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	321
1	43	229
2	85	229
3	126	229
4	211	229
5	394	229
6	898	229
7	1667	229
8	2330	229
9	2545	229
10	3129	229

Stop Event

1×

saturated

Counts

74 → 58

prune35.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 (-.f64 2 y) x))) 2))
✓	0.0b	(-.f64 (/.f64 x (-.f64 (-.f64 2 y) x)) (/.f64 y (-.f64 (-.f64 2 y) x)))
	42.0b	(fma.f64 (/.f64 x y) -2 (+.f64 1 (/.f64 2 y)))
✓	38.8b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))

Compiler

Compiled 1054 to 704 computations (33.2% saved)

regimes184.0ms (5.7%)

Accuracy

Total 0.0b remaining (44%)

Threshold costs 0.0b (44%)

Counts

72 → 1

Compiler

Compiled 3181 to 2251 computations (29.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	15	22
2	27	22
3	33	22
4	36	22

Stop Event

1×

saturated

end69.0ms (2.1%)

Compiler: Compiled 100 to 67 computations (33% saved)

Details

analyze52.0ms (1.6%)

sample852.0ms (26.3%)

simplify28.0ms (0.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.4%)

rewrite117.0ms (3.6%)

simplify35.0ms (1.1%)

prune285.0ms (8.8%)

localize8.0ms (0.2%)

series38.0ms (1.2%)

rewrite83.0ms (2.6%)

simplify61.0ms (1.9%)

prune266.0ms (8.2%)

localize9.0ms (0.3%)

series403.0ms (12.4%)

rewrite69.0ms (2.1%)

simplify108.0ms (3.3%)

prune420.0ms (12.9%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite45.0ms (1.4%)

simplify39.0ms (1.2%)

prune35.0ms (1.1%)

regimes184.0ms (5.7%)

simplify2.0ms (0.1%)

end69.0ms (2.1%)

Profiling