Details

analyze748.0ms (10.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
28.1%	71.8%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.7%	52.2%	0.1%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample4.1s (58.3%)

Results

2.2s	4015×	body	8192	exit
740.0ms	6748×	body	128	valid
452.0ms	4042×	body	128	invalid
223.0ms	762×	body	256	valid
205.0ms	721×	body	512	valid
9.0ms	25×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

prune3.0ms (0%)

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

11.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.4b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
▶	11.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	4.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series48.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

17.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
16.0ms	(/.f64 x (exp.f64 wj))
14.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite78.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

528×	`fma-def_binary64`
354×	`fma-neg_binary64`
218×	`log1p-udef_binary64`
217×	`expm1-udef_binary64`
162×	`egg-rr`

Counts

3 → 162

Calls

3 calls:

74.0ms	(/.f64 x (exp.f64 wj))
74.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
74.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	232	39
2	3478	39
3	5008	39
0	0	0
1	0	0

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
570×	`sub-neg_binary64`
284×	`associate--l+_binary64`
259×	`fma-def_binary64`
245×	`associate--r+_binary64`

Counts

214 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	1071
1	243	1062
2	736	1046
3	2794	1040
4	4672	1040
5	4972	1040

prune183.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	203	5	208

Error

0.1b

Counts

208 → 5

Alt Table

Status	Error	Program
	12.4b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))) wj)
	11.9b	(fma.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (fma.f64 wj wj (-.f64 1 wj)) wj)
	51.7b	(pow.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3) 1/3)
	11.9b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)
▶	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))

Compiler

Compiled 4340 to 2109 computations (51.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	0.2b	(*.f64 8/3 (pow.f64 wj 3))
✓	6.1b	(.f64 x (.f64 wj wj))

series59.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

27.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
22.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
7.0ms	(.f64 x (.f64 wj wj))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite100.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

977×	`prod-diff_binary64`
162×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
153×	`add-cbrt-cube_binary64`

Counts

4 → 106

Calls

4 calls:

97.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
97.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
97.0ms	(*.f64 8/3 (pow.f64 wj 3))
97.0ms	(.f64 x (.f64 wj wj))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	67
1	340	67
2	3800	67
3	5605	67
0	0	0
1	0	0

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-neg_binary64`
853×	`sub-neg_binary64`
355×	`fma-def_binary64`
310×	`cancel-sign-sub-inv_binary64`
300×	`associate-+l-_binary64`

Counts

178 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	1354
1	142	1214
2	536	1168
3	1811	1130
4	4590	1130
5	5452	1130

prune181.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	132	7	139

Error

0.1b

Counts

139 → 7

Alt Table

Status	Error	Program
	31.9b	(fma.f64 (sqrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (sqrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	49.8b	(pow.f64 (pow.f64 (-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))) 3) 1/3)
	12.4b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))) wj)
▶	11.9b	(fma.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (fma.f64 wj wj (-.f64 1 wj)) wj)
	51.7b	(pow.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3) 1/3)
	11.9b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)
✓	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))

Compiler

Compiled 5076 to 2874 computations (43.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3)))
✓	0.0b	(fma.f64 wj wj (-.f64 1 wj))
	0.0b	(/.f64 x (exp.f64 wj))
✓	4.8b	(fma.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (fma.f64 wj wj (-.f64 1 wj)) wj)

series80.0ms (1.1%)

Counts

3 → 60

Calls

3 calls:

45.0ms

(fma.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (fma.f64 wj wj (-.f64 1 wj)) wj)

30.0ms

(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3)))

4.0ms

(fma.f64 wj wj (-.f64 1 wj))

rewrite77.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

280×	`expm1-udef_binary64`
279×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

3 → 88

Calls

3 calls:

75.0ms

(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3)))

75.0ms

(fma.f64 wj wj (-.f64 1 wj))

75.0ms

(fma.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (fma.f64 wj wj (-.f64 1 wj)) wj)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	313	55
2	4240	55
3	4999	55
0	0	0
1	0	0

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
699×	`fma-neg_binary64`
539×	`sub-neg_binary64`
274×	`fma-def_binary64`
226×	`associate--l+_binary64`

Counts

148 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1928
1	291	1874
2	897	1708
3	3236	1707
4	4958	1707
5	5466	1707

prune165.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	176	7	183

Error

0.1b

Counts

183 → 7

Alt Table

Status	Error	Program
	31.9b	(fma.f64 (sqrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (sqrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	49.8b	(pow.f64 (pow.f64 (-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))) 3) 1/3)
	12.4b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))) wj)
✓	11.9b	(fma.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (fma.f64 wj wj (-.f64 1 wj)) wj)
	51.7b	(pow.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3) 1/3)
▶	11.9b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)
✓	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))

Compiler

Compiled 4733 to 2543 computations (46.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 wj 1))
	0.0b	(/.f64 x (exp.f64 wj))
✓	4.8b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)

series17.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

15.0ms	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)
2.0ms	(/.f64 1 (+.f64 wj 1))

rewrite56.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

814×	`prod-diff_binary64`
199×	`log1p-udef_binary64`
198×	`expm1-udef_binary64`
112×	`add-sqr-sqrt_binary64`
107×	`log1p-expm1-u_binary64`

Counts

2 → 49

Calls

2 calls:

55.0ms	(/.f64 1 (+.f64 wj 1))
55.0ms	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	221	25
2	2903	25
3	4983	25
0	0	0
1	0	0

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

427×	`associate--l+_binary64`
387×	`associate-+l-_binary64`
367×	`associate-l_binary64`
339×	`fma-neg_binary64`
312×	`times-frac_binary64`

Counts

85 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	638
1	170	630
2	479	623
3	1564	621
4	4379	621
5	4969	621
6	4998	621
7	4947	621

prune96.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	120	7	127

Error

0.1b

Counts

127 → 7

Alt Table

Status	Error	Program
	31.9b	(fma.f64 (sqrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (sqrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	49.8b	(pow.f64 (pow.f64 (-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))) 3) 1/3)
	12.4b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))) wj)
✓	11.9b	(fma.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (fma.f64 wj wj (-.f64 1 wj)) wj)
	51.7b	(pow.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3) 1/3)
✓	11.9b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)
✓	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))

Compiler

Compiled 2236 to 1129 computations (49.5% saved)

regimes419.0ms (5.9%)

Accuracy

Total 0.5b remaining (83.6%)

Threshold costs 0.5b (83.6%)

Counts

120 → 2

Compiler

Compiled 7323 to 4734 computations (35.4% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 18 to 8 computations (55.6% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

56×	`distribute-rgt-neg-in_binary64`
48×	`cancel-sign-sub-inv_binary64`
38×	`neg-sub0_binary64`
38×	`neg-mul-1_binary64`
37×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	90
1	54	90
2	74	90
3	92	90
4	118	90
5	134	90
6	153	90
7	179	90
8	210	90
9	240	90
10	271	90
11	297	90
12	318	90
13	331	90
14	338	90
15	343	90
16	345	90
17	341	90

end152.0ms (2.2%)

Compiler: Compiled 299 to 186 computations (37.8% saved)

Iter	Nodes	Cost
0	34	90
1	54	90
2	74	90
3	92	90
4	118	90
5	134	90
6	153	90
7	179	90
8	210	90
9	240	90
10	271	90
11	297	90
12	318	90
13	331	90
14	338	90
15	343	90
16	345	90
17	341	90

Iter	Nodes	Cost
0	34	90
1	54	90
2	74	90
3	92	90
4	118	90
5	134	90
6	153	90
7	179	90
8	210	90
9	240	90
10	271	90
11	297	90
12	318	90
13	331	90
14	338	90
15	343	90
16	345	90
17	341	90

Details

analyze748.0ms (10.6%)

sample4.1s (58.3%)

simplify80.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series48.0ms (0.7%)

rewrite78.0ms (1.1%)

simplify69.0ms (1%)

prune183.0ms (2.6%)

localize17.0ms (0.2%)

series59.0ms (0.8%)

rewrite100.0ms (1.4%)

simplify83.0ms (1.2%)

prune181.0ms (2.6%)

localize13.0ms (0.2%)

series80.0ms (1.1%)

rewrite77.0ms (1.1%)

simplify90.0ms (1.3%)

prune165.0ms (2.3%)

localize8.0ms (0.1%)

series17.0ms (0.2%)

rewrite56.0ms (0.8%)

simplify96.0ms (1.4%)

prune96.0ms (1.4%)

regimes419.0ms (5.9%)

bsearch4.0ms (0.1%)

simplify15.0ms (0.2%)

end152.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	34	90
1	54	90
2	74	90
3	92	90
4	118	90
5	134	90
6	153	90
7	179	90
8	210	90
9	240	90
10	271	90
11	297	90
12	318	90
13	331	90
14	338	90
15	343	90
16	345	90
17	341	90