Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.5s (38.9%)

Results

633.0ms	2053×	body	1024	valid
428.0ms	4425×	body	128	valid
251.0ms	1001×	body	512	valid
93.0ms	552×	body	256	valid
82.0ms	225×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

preprocess72.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

859×	`fma-neg_binary64`
764×	`fma-def_binary64`
321×	`div-sub_binary64`
169×	`associate-/l*_binary64`
149×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	60	19
5	100	19
6	205	19
7	377	19
8	951	19
9	2127	19
10	2751	19
11	3062	19
12	3879	19
13	4173	19
14	4215	19
15	4217	19
16	4219	19
17	4229	19
18	4229	19
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify66.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
764×	`fma-def_binary64`
321×	`div-sub_binary64`
169×	`associate-/l*_binary64`
149×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	60	19
5	100	19
6	205	19
7	377	19
8	951	19
9	2127	19
10	2751	19
11	3062	19
12	3879	19
13	4173	19
14	4215	19
15	4217	19
16	4219	19
17	4229	19
18	4229	19

Stop Event

1×

saturated

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

28.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

2.0ms	(/.f64 x (+.f64 x 1))	x	inf
1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	-inf
1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	inf
1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	0
1.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))	x	-inf

rewrite79.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

470×	`fma-def_binary64`
286×	`fma-neg_binary64`
267×	`log-div_binary64`
210×	`egg-rr`
174×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	195	36
2	3184	36

Stop Event

1×	node limit

Counts

3 → 210

simplify32.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

405×	`fma-neg_binary64`
344×	`cancel-sign-sub-inv_binary64`
288×	`fma-def_binary64`
287×	`associate-l_binary64`
233×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	475
1	204	443
2	627	430
3	1940	428

Stop Event

1×	node limit

Counts

246 → 250

prune245.0ms (6.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	246	4	250
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	247	4	251

Error

0.0b

Counts

251 → 4

Alt Table

Status	Error	Program
	28.6b	(/.f64 (-.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))
	32.9b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
▶	28.5b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))))
	61.6b	(fma.f64 (+.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (-.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 x -1))) (+.f64 x 1) (/.f64 (+.f64 x 1) (+.f64 x -1))))

Compiler

Compiled 6232 to 4587 computations (26.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))))
✓	0.0b	(pow.f64 (/.f64 x (+.f64 x 1)) 2)
✓	0.0b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)
✓	3.0b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))

series13.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

2.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))))	x	-inf
1.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))))	x	inf
1.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))	x	inf
1.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))	x	-inf
1.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))	x	0

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

167×	`egg-rr`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-sqr-sqrt_binary64`
157×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	94
1	334	67

Stop Event

1×	node limit

Counts

4 → 167

simplify40.0ms (1%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-neg_binary64`
458×	`cancel-sign-sub-inv_binary64`
424×	`fma-def_binary64`
216×	`sub-neg_binary64`
156×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	696
1	309	653
2	947	640
3	3043	638

Stop Event

1×	node limit

Counts

215 → 221

prune202.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	221	4	225

Error

0.0b

Counts

225 → 4

Alt Table

Status	Error	Program
▶	28.6b	(/.f64 (-.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))
	32.9b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	28.5b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))))
	61.6b	(fma.f64 (+.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (-.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 x -1))) (+.f64 x 1) (/.f64 (+.f64 x 1) (+.f64 x -1))))

Compiler

Compiled 7896 to 5905 computations (25.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1))
✓	0.0b	(*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))
✓	0.3b	(/.f64 (-.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))
✓	2.9b	(-.f64 (+.f64 x -1) (*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1)))

series8.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

1.0ms	(/.f64 (-.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))	x	-inf
1.0ms	(/.f64 (-.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))	x	inf
1.0ms	(*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1))	x	inf
1.0ms	(*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1))	x	-inf
1.0ms	(/.f64 (-.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))	x	0

rewrite87.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

228×	`log1p-udef_binary64`
189×	`egg-rr`
136×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	79
1	271	60
2	4651	60

Stop Event

1×	node limit

Counts

4 → 189

simplify32.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

532×	`times-frac_binary64`
437×	`cancel-sign-sub-inv_binary64`
380×	`fma-def_binary64`
303×	`associate-/l/_binary64`
205×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	429
1	112	392
2	300	388
3	846	388
4	2454	385

Stop Event

1×	node limit

Counts

237 → 217

prune194.0ms (5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	217	4	221

Error

0.0b

Counts

221 → 4

Alt Table

Status	Error	Program
✓	28.6b	(/.f64 (-.f64 (+.f64 x -1) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))
	32.9b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	28.5b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))))
▶	0.3b	(/.f64 (-.f64 (/.f64 -1 x) 3) (*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))

Compiler

Compiled 6022 to 4259 computations (29.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) x)
	0.0b	(*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1))
✓	0.3b	(/.f64 (-.f64 (/.f64 -1 x) 3) (*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

2.0ms	(/.f64 (+.f64 x 1) x)	x	-inf
1.0ms	(/.f64 (-.f64 (/.f64 -1 x) 3) (*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))	x	inf
1.0ms	(/.f64 (-.f64 (/.f64 -1 x) 3) (*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))	x	-inf
1.0ms	(/.f64 (-.f64 (/.f64 -1 x) 3) (*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))	x	0
1.0ms	(/.f64 (+.f64 x 1) x)	x	inf

rewrite102.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

579×	`prod-diff_binary64`
198×	`egg-rr`
141×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	287	24
2	4386	24

Stop Event

1×	node limit

Counts

2 → 198

simplify31.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

531×	`times-frac_binary64`
424×	`cancel-sign-sub-inv_binary64`
377×	`fma-def_binary64`
275×	`associate-/l/_binary64`
195×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	261
1	94	242
2	267	238
3	802	238
4	2398	235

Stop Event

1×	node limit

Counts

222 → 214

prune288.0ms (7.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	265	3	268

Error

Counts

268 → 3

Alt Table

Status	Error	Program
✓	28.5b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))))
✓	0.3b	(/.f64 (-.f64 (/.f64 -1 x) 3) (*.f64 (/.f64 (+.f64 x 1) x) (+.f64 x -1)))
	14.5b	(*.f64 (+.f64 (neg.f64 (/.f64 -1 x)) 3) (/.f64 1 (/.f64 (neg.f64 (fma.f64 x x -1)) x)))

Compiler

Compiled 10471 to 7333 computations (30% saved)

regimes692.0ms (17.9%)

Accuracy

Total 0.1b remaining (86.5%)

Threshold costs 0.1b (86.5%)

Counts

348 → 1

Compiler

Compiled 14230 to 10546 computations (25.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	19	22
2	20	22

Stop Event

1×

saturated

end64.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 97 to 73 computations (24.7% saved)

Details

analyze6.0ms (0.1%)

sample1.5s (38.9%)

preprocess72.0ms (1.9%)

simplify66.0ms (1.7%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series8.0ms (0.2%)

rewrite79.0ms (2%)

simplify32.0ms (0.8%)

prune245.0ms (6.4%)

localize11.0ms (0.3%)

series13.0ms (0.3%)

rewrite54.0ms (1.4%)

simplify40.0ms (1%)

prune202.0ms (5.2%)

localize10.0ms (0.3%)

series8.0ms (0.2%)

rewrite87.0ms (2.3%)

simplify32.0ms (0.8%)

prune194.0ms (5%)

localize8.0ms (0.2%)

series6.0ms (0.1%)

rewrite102.0ms (2.7%)

simplify31.0ms (0.8%)

prune288.0ms (7.5%)

regimes692.0ms (17.9%)

simplify2.0ms (0.1%)

end64.0ms (1.7%)

Profiling