Details

analyze757.0ms (10.5%)

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)

sample4.0s (54.7%)

Results

2.1s	3990×	body	8192	exit
831.0ms	6736×	body	128	valid
452.0ms	4090×	body	128	invalid
224.0ms	708×	body	256	valid
218.0ms	779×	body	512	valid
12.0ms	33×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify78.0ms (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

15.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	15.8b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

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))
✓	5.6b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series46.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

18.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
14.0ms	(/.f64 x (exp.f64 wj))
13.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite76.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

159× egg-rr

Counts

3 → 159

Calls

2 calls:

70.0ms	((+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 x (exp.f64 wj)))
0.0ms	()

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

simplify68.0ms (0.9%)

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

211 → 203

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

prune163.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	202	3	205

Error

0.1b

Counts

205 → 3

Alt Table

Status	Error	Program
	7.3b	(+.f64 (-.f64 wj (/.f64 wj (+.f64 wj 1))) (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))))
▶	1.7b	(-.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)))
	35.3b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

Compiler

Compiled 4250 to 2051 computations (51.7% saved)

localize14.0ms (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)))
✓	0.1b	(*.f64 8/3 (pow.f64 wj 3))
✓	6.3b	(.f64 x (.f64 wj wj))

series57.0ms (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)))
19.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
8.0ms	(.f64 x (.f64 wj wj))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite77.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

102× egg-rr

Counts

4 → 102

Calls

2 calls:

72.0ms

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

0.0ms

()

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

simplify77.0ms (1.1%)

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

174 → 130

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

prune155.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	127	6	133

Error

0.1b

Counts

133 → 6

Alt Table

Status	Error	Program
▶	7.3b	(+.f64 (-.f64 wj (/.f64 wj (+.f64 wj 1))) (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))))
	53.7b	(fma.f64 wj (-.f64 wj (.f64 (.f64 wj wj) (fma.f64 x 8/3 1))) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2)))
✓	1.7b	(-.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)))
	28.2b	(pow.f64 (sqrt.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)))) 2)
	51.0b	(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)
	35.3b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

Compiler

Compiled 4944 to 2804 computations (43.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
✓	0.0b	(/.f64 wj (+.f64 wj 1))
✓	0.0b	(*.f64 (exp.f64 wj) (+.f64 wj 1))
✓	5.3b	(-.f64 wj (/.f64 wj (+.f64 wj 1)))

series29.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

22.0ms	(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
2.0ms	(*.f64 (exp.f64 wj) (+.f64 wj 1))
2.0ms	(-.f64 wj (/.f64 wj (+.f64 wj 1)))
2.0ms	(/.f64 wj (+.f64 wj 1))

rewrite106.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

255× egg-rr

Counts

4 → 255

Calls

2 calls:

96.0ms	((-.f64 wj (/.f64 wj (+.f64 wj 1))) (.f64 (exp.f64 wj) (+.f64 wj 1)) (/.f64 wj (+.f64 wj 1)) (/.f64 x (.f64 (exp.f64 wj) (+.f64 wj 1))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	227	36
2	3247	36
3	5291	36
0	0	0
1	0	0

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

603×	`cancel-sign-sub-inv_binary64`
532×	`times-frac_binary64`
408×	`fma-neg_binary64`
236×	`fma-def_binary64`
228×	`sub-neg_binary64`

Counts

315 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	812
1	212	803
2	602	786
3	1735	783
4	4314	783
5	4979	783
6	4945	783

prune293.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	3	1	4
Picked	0	1	1
Done	1	0	1
Total	311	3	314

Error

0.0b

Counts

314 → 3

Alt Table

Status	Error	Program
✓	7.3b	(+.f64 (-.f64 wj (/.f64 wj (+.f64 wj 1))) (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))))
▶	0.8b	(+.f64 (-.f64 (fma.f64 wj wj (pow.f64 wj 4)) (pow.f64 wj 3)) (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))))
	35.3b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

Compiler

Compiled 10311 to 5877 computations (43% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 wj wj (pow.f64 wj 4))
	0.0b	(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
	0.0b	(*.f64 (exp.f64 wj) (+.f64 wj 1))
✓	0.0b	(-.f64 (fma.f64 wj wj (pow.f64 wj 4)) (pow.f64 wj 3))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(-.f64 (fma.f64 wj wj (pow.f64 wj 4)) (pow.f64 wj 3))
3.0ms	(fma.f64 wj wj (pow.f64 wj 4))

rewrite60.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

107× egg-rr

Counts

2 → 107

Calls

2 calls:

57.0ms	((-.f64 (fma.f64 wj wj (pow.f64 wj 4)) (pow.f64 wj 3)) (fma.f64 wj wj (pow.f64 wj 4)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	180	22
2	1961	22
3	6027	22
0	0	0
1	0	0

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
706×	`fma-def_binary64`
489×	`distribute-rgt-neg-in_binary64`
370×	`neg-mul-1_binary64`
297×	`cancel-sign-sub-inv_binary64`

Counts

131 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	240
1	31	210
2	80	210
3	256	210
4	825	210
5	2694	210
6	4806	210
7	5010	210

prune245.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	213	3	216

Error

0.0b

Counts

216 → 3

Alt Table

Status	Error	Program
✓	7.3b	(+.f64 (-.f64 wj (/.f64 wj (+.f64 wj 1))) (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))))
✓	0.8b	(+.f64 (-.f64 (fma.f64 wj wj (pow.f64 wj 4)) (pow.f64 wj 3)) (/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1))))
	35.3b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

Compiler

Compiled 6209 to 3113 computations (49.9% saved)

regimes700.0ms (9.7%)

Accuracy

Total 1.1b remaining (93.7%)

Threshold costs 0b (0%)

Counts

203 → 1

Compiler

Compiled 12087 to 8073 computations (33.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	22	28
2	26	28
3	28	28
4	29	28
5	28	28

end77.0ms (1.1%)

Compiler: Compiled 112 to 71 computations (36.6% saved)

Details

analyze757.0ms (10.5%)

sample4.0s (54.7%)

simplify78.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series46.0ms (0.6%)

rewrite76.0ms (1%)

simplify68.0ms (0.9%)

prune163.0ms (2.3%)

localize14.0ms (0.2%)

series57.0ms (0.8%)

rewrite77.0ms (1.1%)

simplify77.0ms (1.1%)

prune155.0ms (2.1%)

localize8.0ms (0.1%)

series29.0ms (0.4%)

rewrite106.0ms (1.5%)

simplify86.0ms (1.2%)

prune293.0ms (4%)

localize11.0ms (0.2%)

series7.0ms (0.1%)

rewrite60.0ms (0.8%)

simplify72.0ms (1%)

prune245.0ms (3.4%)

regimes700.0ms (9.7%)

simplify3.0ms (0%)

end77.0ms (1.1%)

Profiling