Details

analyze245.0ms (8.3%)

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 11 to 7 computations (36.4% saved)

sample1.0s (34.5%)

Results

905.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify72.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
621×	`fma-neg_binary64`
457×	`times-frac_binary64`
316×	`div-sub_binary64`
141×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	18	12
2	38	12
3	71	12
4	152	12
5	207	12
6	597	10
7	937	10
8	1314	10
9	1337	10
10	1342	10
11	1369	10
12	1379	10
13	1379	10
14	1274	10

prune2.0ms (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 f n) (-.f64 n f))

Compiler

Compiled 35 to 18 computations (48.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(/.f64 (+.f64 f n) (-.f64 n f))

rewrite49.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

884×	`expm1-log1p-u_binary64`
758×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
74×	`log1p-expm1-u_binary64`
72×	`add-log-exp_binary64`

Counts

1 → 35

Calls

1 calls:

48.0ms

(/.f64 (+.f64 f n) (-.f64 n f))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	143	10
2	2146	10
3	5253	10
0	0	0
1	0	0

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary64`
821×	`associate-/l*_binary64`
515×	`associate-/r*_binary64`
386×	`associate-/r/_binary64`
251×	`cancel-sign-sub-inv_binary64`

Counts

59 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	426
1	110	393
2	368	342
3	1432	324
4	4696	324
5	5368	324

prune29.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	2	50

Error

0.0b

Counts

50 → 2

Alt Table

Status	Error	Program
▶	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
	43.4b	(.f64 (/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3))) (fma.f64 n n (.f64 f (+.f64 f n))))

Compiler

Compiled 705 to 292 computations (58.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
✓	0.0b	(/.f64 (-.f64 n f) (+.f64 f n))

series21.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
9.0ms	(/.f64 (-.f64 n f) (+.f64 f n))

rewrite133.0ms (4.5%)

Algorithm

2×	batch-egg-rewrite

Rules

974×	`prod-diff_binary64`
280×	`egg-rr`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
98×	`add-sqr-sqrt_binary64`

Counts

2 → 280

Calls

2 calls:

121.0ms	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
121.0ms	(/.f64 (-.f64 n f) (+.f64 f n))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	188	20
2	2665	20
3	5122	20
0	0	0
1	0	0

simplify64.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

758×	`cancel-sign-sub-inv_binary64`
468×	`fma-neg_binary64`
313×	`neg-mul-1_binary64`
307×	`neg-sub0_binary64`
269×	`distribute-neg-frac_binary64`

Counts

328 → 306

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	852
1	152	792
2	497	702
3	1860	651
4	4281	651
5	4974	651

prune162.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	305	1	306
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	305	3	308

Error

Counts

308 → 3

Alt Table

Status	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
	43.4b	(.f64 (/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3))) (fma.f64 n n (.f64 f (+.f64 f n))))
▶	31.8b	(/.f64 (sqrt.f64 (+.f64 n f)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f))))

Compiler

Compiled 13238 to 3434 computations (74.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 n f))
✓	0.0b	(/.f64 (sqrt.f64 (+.f64 n f)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f))))
✓	0.2b	(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f)))

series64.0ms (2.2%)

Counts

3 → 40

Calls

3 calls:

35.0ms	(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f)))
18.0ms	(sqrt.f64 (+.f64 n f))
10.0ms	(/.f64 (sqrt.f64 (+.f64 n f)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f))))

rewrite129.0ms (4.4%)

Algorithm

2×	batch-egg-rewrite

Rules

752×	`prod-diff_binary64`
614×	`fma-udef_binary64`
238×	`fma-neg_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Counts

3 → 130

Calls

3 calls:

125.0ms	(sqrt.f64 (+.f64 n f))
125.0ms	(/.f64 (sqrt.f64 (+.f64 n f)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f))))
125.0ms	(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	38
1	188	28
2	2807	28
3	4774	28
4	4661	28
5	5052	28
0	0	0
1	0	0

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
412×	`fma-def_binary64`
317×	`distribute-rgt-neg-in_binary64`
315×	`distribute-lft-neg-in_binary64`
285×	`neg-mul-1_binary64`

Counts

170 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	856
1	293	823
2	920	760
3	3042	742
4	4848	742
5	5077	742

prune84.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	211	3	214

Error

Counts

214 → 3

Alt Table

Status	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
▶	43.4b	(.f64 (/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3))) (fma.f64 n n (.f64 f (+.f64 f n))))
✓	31.8b	(/.f64 (sqrt.f64 (+.f64 n f)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f))))

Compiler

Compiled 4657 to 1618 computations (65.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 n n (*.f64 f (+.f64 f n)))
✓	3.5b	(-.f64 (pow.f64 n 3) (pow.f64 f 3))
✓	10.6b	(/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3)))
✓	31.7b	(.f64 (/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3))) (fma.f64 n n (.f64 f (+.f64 f n))))

series45.0ms (1.5%)

Counts

4 → 78

Calls

4 calls:

14.0ms	(/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3)))
13.0ms	(.f64 (/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3))) (fma.f64 n n (.f64 f (+.f64 f n))))
11.0ms	(-.f64 (pow.f64 n 3) (pow.f64 f 3))
6.0ms	(fma.f64 n n (*.f64 f (+.f64 f n)))

rewrite87.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

549×	`fma-def_binary64`
250×	`fma-neg_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
187×	`egg-rr`

Counts

4 → 187

Calls

4 calls:

83.0ms	(fma.f64 n n (*.f64 f (+.f64 f n)))
83.0ms	(-.f64 (pow.f64 n 3) (pow.f64 f 3))
83.0ms	(/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3)))
83.0ms	(.f64 (/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3))) (fma.f64 n n (.f64 f (+.f64 f n))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	66
1	276	47
2	3708	47
3	5154	47
0	0	0
1	0	0

simplify116.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

463×	`cancel-sign-sub-inv_binary64`
307×	`fma-neg_binary64`
253×	`neg-mul-1_binary64`
246×	`neg-sub0_binary64`
240×	`times-frac_binary64`

Counts

265 → 233

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	1296
1	197	1167
2	679	1116
3	2538	1098
4	4416	1098
5	4983	1098
6	4999	1098
7	4951	1098

prune203.0ms (6.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	233	3	236

Error

Counts

236 → 3

Alt Table

Status	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
✓	43.4b	(.f64 (/.f64 (+.f64 f n) (-.f64 (pow.f64 n 3) (pow.f64 f 3))) (fma.f64 n n (.f64 f (+.f64 f n))))
✓	31.8b	(/.f64 (sqrt.f64 (+.f64 n f)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 n f))))

Compiler

Compiled 5901 to 2513 computations (57.4% saved)

regimes137.0ms (4.7%)

Accuracy

Total 0.0b remaining (26.4%)

Threshold costs 0.0b (26.4%)

Counts

36 → 1

Compiler

Compiled 1422 to 924 computations (35% 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

end136.0ms (4.6%)

Compiler: Compiled 70 to 40 computations (42.9% saved)

Details

analyze245.0ms (8.3%)

sample1.0s (34.5%)

simplify72.0ms (2.4%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite49.0ms (1.7%)

simplify53.0ms (1.8%)

prune29.0ms (1%)

localize5.0ms (0.2%)

series21.0ms (0.7%)

rewrite133.0ms (4.5%)

simplify64.0ms (2.2%)

prune162.0ms (5.5%)

localize6.0ms (0.2%)

series64.0ms (2.2%)

rewrite129.0ms (4.4%)

simplify65.0ms (2.2%)

prune84.0ms (2.8%)

localize11.0ms (0.4%)

series45.0ms (1.5%)

rewrite87.0ms (2.9%)

simplify116.0ms (3.9%)

prune203.0ms (6.9%)

regimes137.0ms (4.7%)

simplify2.0ms (0.1%)

end136.0ms (4.6%)

Profiling