Details

analyze134.0ms (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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
50%	50%	0.1%	7
67.1%	32.8%	0.1%	8
74.9%	25%	0.1%	9
83.9%	16%	0.1%	10
87.4%	12.5%	0.1%	11
92%	7.9%	0.1%	12
93.7%	6.2%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample857.0ms (19.3%)

Results

846.0ms	8255×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

preprocess36.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

762×	`fma-neg_binary64`
509×	`div-sub_binary64`
413×	`fma-def_binary64`
327×	`cancel-sign-sub-inv_binary64`
304×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	28	32
2	43	28
3	65	28
4	95	28
5	165	28
6	292	28
7	557	28
8	1111	28
9	1847	28
10	3014	28
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1119×	`fma-neg_binary64`
675×	`div-sub_binary64`
519×	`fma-def_binary64`
403×	`associate-/l*_binary64`
249×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	60	14
5	96	14
6	172	14
7	254	14
8	492	14
9	1053	14
10	1774	14
11	3750	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
▶	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))

Compiler

Compiled 73 to 52 computations (28.8% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 x y) 2)
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
✓	0.0b	(+.f64 1 (/.f64 (*.f64 x y) 2))
✓	6.2b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

series28.0ms (0.6%)

Counts

4 → 96

Calls

24 calls:

2.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))	x	-inf
2.0ms	(/.f64 (*.f64 x y) 2)	y	-inf
2.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))	y	-inf
2.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))	y	inf
2.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))	x	0

rewrite112.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`prod-diff_binary64`
211×	`egg-rr`
202×	`log1p-udef_binary64`
113×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	230	40
2	3221	40

Stop Event

1×	node limit

Counts

4 → 211

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
399×	`distribute-rgt-neg-in_binary64`
238×	`fma-def_binary64`
222×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1372
1	210	1358
2	689	1348
3	2912	1335

Stop Event

1×	node limit

Counts

307 → 247

prune206.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	245	2	247
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	246	3	249

Error

0.0b

Counts

249 → 3

Alt Table

Status	Error	Program
	17.3b	(+.f64 (fma.f64 1 x (neg.f64 (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3)))))) (fma.f64 (neg.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2)))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))))))
	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
▶	0.0b	(-.f64 x (/.f64 y (fma.f64 y (*.f64 1/2 x) 1)))

Compiler

Compiled 7780 to 4640 computations (40.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 y (*.f64 1/2 x) 1)))
✓	6.2b	(/.f64 y (fma.f64 y (*.f64 1/2 x) 1))

series17.0ms (0.4%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(-.f64 x (/.f64 y (fma.f64 y (*.f64 1/2 x) 1)))	y	inf
2.0ms	(-.f64 x (/.f64 y (fma.f64 y (*.f64 1/2 x) 1)))	y	-inf
2.0ms	(-.f64 x (/.f64 y (fma.f64 y (*.f64 1/2 x) 1)))	x	0
2.0ms	(/.f64 y (fma.f64 y (*.f64 1/2 x) 1))	y	-inf
1.0ms	(/.f64 y (fma.f64 y (*.f64 1/2 x) 1))	y	inf

rewrite108.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

532×	`prod-diff_binary64`
459×	`log-prod_binary64`
222×	`fma-def_binary64`
188×	`egg-rr`
172×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	191	25
2	2534	25

Stop Event

1×	node limit

Counts

2 → 188

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
402×	`distribute-rgt-neg-in_binary64`
239×	`fma-def_binary64`
219×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1030
1	201	1016
2	676	1006
3	2943	993

Stop Event

1×	node limit

Counts

236 → 220

prune258.0ms (5.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	220	3	223

Error

Counts

223 → 3

Alt Table

Status	Error	Program
	17.3b	(+.f64 (fma.f64 1 x (neg.f64 (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3)))))) (fma.f64 (neg.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2)))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))))))
	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
▶	0.0b	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))

Compiler

Compiled 7422 to 4872 computations (34.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))
✓	0.1b	(pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1)
✓	6.1b	(/.f64 (fma.f64 y (*.f64 1/2 x) 1) y)

series26.0ms (0.6%)

Counts

3 → 72

Calls

18 calls:

3.0ms	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))	x	inf
2.0ms	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))	y	-inf
2.0ms	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))	y	inf
2.0ms	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))	x	0
2.0ms	(pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1)	y	-inf

rewrite85.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

462×	`prod-diff_binary64`
217×	`egg-rr`
215×	`fma-def_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	233	36
2	2982	36

Stop Event

1×	node limit

Counts

3 → 217

simplify47.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
401×	`distribute-rgt-neg-in_binary64`
234×	`fma-def_binary64`
221×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1234
1	205	1184
2	680	1174
3	2930	1161

Stop Event

1×	node limit

Counts

289 → 253

prune314.0ms (7.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	253	3	256

Error

Counts

256 → 3

Alt Table

Status	Error	Program
	17.3b	(+.f64 (fma.f64 1 x (neg.f64 (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3)))))) (fma.f64 (neg.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2)))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))))))
▶	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))

Compiler

Compiled 7961 to 5416 computations (32% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(fma.f64 x -1/2 (/.f64 -1 y))
✓	0.1b	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))

series22.0ms (0.5%)

Counts

3 → 72

Calls

18 calls:

3.0ms	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))	x	0
2.0ms	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))	y	-inf
2.0ms	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))	x	0
2.0ms	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))	y	inf
1.0ms	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))	y	inf

rewrite67.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`prod-diff_binary64`
204×	`fma-def_binary64`
178×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`
152×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	198	33
2	2589	33

Stop Event

1×	node limit

Counts

3 → 149

simplify47.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
236×	`fma-def_binary64`
216×	`associate-r_binary64`
210×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1270
1	214	1220
2	704	1174
3	2960	1165

Stop Event

1×	node limit

Counts

221 → 186

prune214.0ms (4.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
	17.3b	(+.f64 (fma.f64 1 x (neg.f64 (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3)))))) (fma.f64 (neg.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2)))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (.f64 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2))) (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))))))
✓	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(-.f64 x (pow.f64 (/.f64 (fma.f64 y (*.f64 1/2 x) 1) y) -1))

Compiler

Compiled 4221 to 3122 computations (26% saved)

regimes1.6s (36.3%)

Accuracy

Total 0.0b remaining (88.5%)

Threshold costs 0.0b (88.5%)

Counts

320 → 1

Compiler

Compiled 35378 to 25286 computations (28.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	22	41
2	28	41
3	31	41
4	32	41

Stop Event

1×

saturated

end95.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 177 to 126 computations (28.8% saved)

Details

analyze134.0ms (3%)

sample857.0ms (19.3%)

preprocess36.0ms (0.8%)

simplify28.0ms (0.6%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series28.0ms (0.6%)

rewrite112.0ms (2.5%)

simplify55.0ms (1.2%)

prune206.0ms (4.6%)

localize6.0ms (0.1%)

series17.0ms (0.4%)

rewrite108.0ms (2.4%)

simplify45.0ms (1%)

prune258.0ms (5.8%)

localize8.0ms (0.2%)

series26.0ms (0.6%)

rewrite85.0ms (1.9%)

simplify47.0ms (1.1%)

prune314.0ms (7.1%)

localize6.0ms (0.1%)

series22.0ms (0.5%)

rewrite67.0ms (1.5%)

simplify47.0ms (1.1%)

prune214.0ms (4.8%)

regimes1.6s (36.3%)

simplify3.0ms (0.1%)

end95.0ms (2.1%)

Profiling