Details

analyze777.0ms (10.2%)

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
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)

sample3.9s (51.9%)

Results

2.2s	4154×	body	8192	exit
788.0ms	6769×	body	128	valid
466.0ms	4109×	body	128	invalid
209.0ms	716×	body	512	valid
159.0ms	746×	body	256	valid
9.0ms	25×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-def_binary64`
481×	`div-sub_binary64`
467×	`fma-neg_binary64`
288×	`associate-/r*_binary64`
282×	`associate-/l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	155	21
4	432	18
5	1495	18
6	4690	18

Stop Event

1×	node limit

Counts

1 → 2

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

12.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.8b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
▶	12.1b	(+.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 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	4.1b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series47.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

18.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
15.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
14.0ms	(/.f64 x (exp.f64 wj))

rewrite69.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	232	39
2	3663	39

Stop Event

1×	node limit

Counts

3 → 159

Calls

3 calls:

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

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
565×	`sub-neg_binary64`
284×	`associate--l+_binary64`
259×	`fma-def_binary64`
242×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	1071
1	245	1062
2	806	1046
3	3297	1040

Stop Event

1×	node limit

Counts

211 → 204

prune162.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	199	5	204
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	201	5	206

Error

0.1b

Counts

206 → 5

Alt Table

Status	Error	Program
	31.7b	(.f64 (-.f64 (.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (/.f64 1 (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
	37.8b	(fma.f64 (sqrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (*.f64 (sqrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (exp.f64 (neg.f64 (log1p.f64 wj)))) wj)
	7.1b	(fma.f64 1 (/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	12.6b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (exp.f64 (neg.f64 (log1p.f64 wj))) wj)
▶	2.8b	(+.f64 (fma.f64 wj wj x) (fma.f64 x (.f64 wj (-.f64 (.f64 wj 5/2) 2)) (.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))))

Compiler

Compiled 4322 to 2061 computations (52.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 wj (-.f64 (.f64 wj 5/2) 2))
✓	0.0b	(+.f64 (fma.f64 wj wj x) (fma.f64 x (.f64 wj (-.f64 (.f64 wj 5/2) 2)) (.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))))
✓	0.3b	(*.f64 x 8/3)
✓	4.9b	(.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))

series38.0ms (0.5%)

Counts

4 → 72

Calls

4 calls:

20.0ms	(+.f64 (fma.f64 wj wj x) (fma.f64 x (.f64 wj (-.f64 (.f64 wj 5/2) 2)) (.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))))
14.0ms	(.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))
3.0ms	(.f64 wj (-.f64 (.f64 wj 5/2) 2))
1.0ms	(*.f64 x 8/3)

rewrite39.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

198×	`add-sqr-sqrt_binary64`
192×	`log1p-expm1-u_binary64`
192×	`expm1-log1p-u_binary64`
189×	`add-cbrt-cube_binary64`
184×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	56
1	417	52

Stop Event

1×	node limit

Counts

4 → 93

Calls

4 calls:

37.0ms	(.f64 wj (-.f64 (.f64 wj 5/2) 2))
37.0ms	(+.f64 (fma.f64 wj wj x) (fma.f64 x (.f64 wj (-.f64 (.f64 wj 5/2) 2)) (.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))))
37.0ms	(*.f64 x 8/3)
37.0ms	(.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

349×	`fma-def_binary64`
296×	`cancel-sign-sub-inv_binary64`
249×	`sub-neg_binary64`
246×	`associate--l+_binary64`
197×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	1290
1	158	1125
2	629	1070
3	2855	1050

Stop Event

1×	node limit

Counts

165 → 123

prune149.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	122	6	128

Error

0.1b

Counts

128 → 6

Alt Table

Status	Error	Program
	31.7b	(.f64 (-.f64 (.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (/.f64 1 (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
▶	2.5b	(+.f64 x (fma.f64 wj wj (-.f64 (.f64 x (.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (.f64 wj -8/3))) 2))) (pow.f64 wj 3))))
	37.8b	(fma.f64 (sqrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (*.f64 (sqrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (exp.f64 (neg.f64 (log1p.f64 wj)))) wj)
	7.1b	(fma.f64 1 (/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	12.6b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (exp.f64 (neg.f64 (log1p.f64 wj))) wj)
✓	2.8b	(+.f64 (fma.f64 wj wj x) (fma.f64 x (.f64 wj (-.f64 (.f64 wj 5/2) 2)) (.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))))

Compiler

Compiled 3740 to 2366 computations (36.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (*.f64 wj -8/3))) 2))
✓	0.0b	(.f64 x (.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (.f64 wj -8/3))) 2)))
✓	0.0b	(.f64 wj (+.f64 5/2 (.f64 wj -8/3)))
✓	0.4b	(*.f64 wj -8/3)

series27.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

19.0ms	(.f64 x (.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (.f64 wj -8/3))) 2)))
3.0ms	(.f64 wj (+.f64 5/2 (.f64 wj -8/3)))
3.0ms	(.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (*.f64 wj -8/3))) 2))
1.0ms	(*.f64 wj -8/3)

rewrite54.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

317×	`prod-diff_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
180×	`fma-neg_binary64`
136×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	273	39
2	3571	39

Stop Event

1×	node limit

Counts

4 → 77

Calls

4 calls:

52.0ms	(.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (*.f64 wj -8/3))) 2))
52.0ms	(.f64 x (.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (.f64 wj -8/3))) 2)))
52.0ms	(.f64 wj (+.f64 5/2 (.f64 wj -8/3)))
52.0ms	(*.f64 wj -8/3)

simplify42.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-neg_binary64`
541×	`fma-def_binary64`
417×	`cancel-sign-sub-inv_binary64`
350×	`distribute-rgt-neg-in_binary64`
193×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	870
1	119	831
2	328	692
3	1088	594
4	3691	594

Stop Event

1×	node limit

Counts

137 → 105

prune138.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	105	6	111

Error

0.1b

Counts

111 → 6

Alt Table

Status	Error	Program
	31.7b	(.f64 (-.f64 (.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (/.f64 1 (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
✓	2.5b	(+.f64 x (fma.f64 wj wj (-.f64 (.f64 x (.f64 wj (-.f64 (.f64 wj (+.f64 5/2 (.f64 wj -8/3))) 2))) (pow.f64 wj 3))))
	37.8b	(fma.f64 (sqrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (*.f64 (sqrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (exp.f64 (neg.f64 (log1p.f64 wj)))) wj)
▶	7.1b	(fma.f64 1 (/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	12.6b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (exp.f64 (neg.f64 (log1p.f64 wj))) wj)
✓	2.8b	(+.f64 (fma.f64 wj wj x) (fma.f64 x (.f64 wj (-.f64 (.f64 wj 5/2) 2)) (.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))))

Compiler

Compiled 2788 to 1794 computations (35.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 wj 1) (exp.f64 wj))
✓	0.0b	(/.f64 wj (+.f64 wj 1))
✓	0.0b	(/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj)))
✓	5.5b	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

series29.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

23.0ms	(/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj)))
2.0ms	(*.f64 (+.f64 wj 1) (exp.f64 wj))
2.0ms	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)
2.0ms	(/.f64 wj (+.f64 wj 1))

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

756×	`prod-diff_binary64`
250×	`egg-rr`
202×	`log1p-udef_binary64`
112×	`add-sqr-sqrt_binary64`
107×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	221	36
2	3271	36

Stop Event

1×	node limit

Counts

4 → 250

Calls

4 calls:

72.0ms	(*.f64 (+.f64 wj 1) (exp.f64 wj))
72.0ms	(/.f64 wj (+.f64 wj 1))
72.0ms	(/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj)))
72.0ms	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

598×	`cancel-sign-sub-inv_binary64`
385×	`fma-neg_binary64`
237×	`associate-+l-_binary64`
233×	`sub-neg_binary64`
218×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	818
1	219	809
2	612	792
3	1961	789

Stop Event

1×	node limit

Counts

310 → 306

prune402.0ms (5.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	303	3	306
Fresh	2	1	3
Picked	1	0	1
Done	1	1	2
Total	307	5	312

Error

0.0b

Counts

312 → 5

Alt Table

Status	Error	Program
✓	2.8b	(+.f64 (fma.f64 wj wj x) (fma.f64 x (.f64 wj (-.f64 (.f64 wj 5/2) 2)) (.f64 (+.f64 (.f64 x 8/3) 1) (neg.f64 (pow.f64 wj 3)))))
	7.1b	(fma.f64 1 (/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj))) (neg.f64 (fma.f64 wj (/.f64 1 (+.f64 wj 1)) (neg.f64 wj))))
	31.7b	(.f64 (-.f64 (.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (/.f64 1 (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
	7.1b	(fma.f64 1 (/.f64 x (.f64 (+.f64 wj 1) (exp.f64 wj))) (neg.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 wj) 2) (.f64 (cbrt.f64 wj) (/.f64 1 (+.f64 wj 1))) (neg.f64 wj)) (fma.f64 (neg.f64 (cbrt.f64 wj)) (pow.f64 (cbrt.f64 wj) 2) wj))))
	1.7b	(fma.f64 1 (/.f64 x (*.f64 (+.f64 wj 1) (exp.f64 wj))) (neg.f64 (+.f64 (pow.f64 wj 3) (-.f64 (pow.f64 wj 5) (fma.f64 wj wj (pow.f64 wj 4))))))

Compiler

Compiled 8995 to 5255 computations (41.6% saved)

regimes1.3s (16.5%)

Accuracy

Total 0.2b remaining (78.7%)

Threshold costs 0.2b (78.7%)

Counts

204 → 2

Compiler

Compiled 13050 to 8766 computations (32.8% saved)

bsearch7.0ms (0.1%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
18×	`sub-neg_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`
15×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	97
1	56	97
2	82	97
3	111	95
4	151	95
5	173	95
6	179	95
7	185	95
8	194	95
9	198	95

Stop Event

1×

saturated

end138.0ms (1.8%)

Compiler: Compiled 276 to 175 computations (36.6% saved)

Details

analyze777.0ms (10.2%)

sample3.9s (51.9%)

simplify29.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series47.0ms (0.6%)

rewrite69.0ms (0.9%)

simplify41.0ms (0.5%)

prune162.0ms (2.1%)

localize16.0ms (0.2%)

series38.0ms (0.5%)

rewrite39.0ms (0.5%)

simplify45.0ms (0.6%)

prune149.0ms (2%)

localize13.0ms (0.2%)

series27.0ms (0.4%)

rewrite54.0ms (0.7%)

simplify42.0ms (0.6%)

prune138.0ms (1.8%)

localize10.0ms (0.1%)

series29.0ms (0.4%)

rewrite77.0ms (1%)

simplify37.0ms (0.5%)

prune402.0ms (5.3%)

regimes1.3s (16.5%)

bsearch7.0ms (0.1%)

simplify6.0ms (0.1%)

end138.0ms (1.8%)

Profiling