Details

analyze56.0ms (1.4%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample730.0ms (18.5%)

Results

718.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 12 computations (40% saved)

preprocess67.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

1022×	`fma-neg_binary64`
485×	`div-sub_binary64`
480×	`times-frac_binary64`
259×	`associate-/l*_binary64`
250×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	22	20
2	34	20
3	54	20
4	104	20
5	192	20
6	319	20
7	676	20
8	1930	20
9	3892	20
10	4645	20
11	4722	20
12	4800	20
13	4830	20
14	4854	20
15	4876	20
16	4902	20
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
511×	`fma-neg_binary64`
363×	`times-frac_binary64`
334×	`div-sub_binary64`
143×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	30	10
4	57	10
5	93	10
6	154	10
7	244	10
8	437	10
9	990	10
10	2383	10
11	3170	10
12	3927	10
13	3974	10
14	3996	10
15	4016	10
16	4016	10

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite108.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`expm1-log1p-u_binary64`
768×	`prod-diff_binary64`
233×	`egg-rr`
76×	`add-sqr-sqrt_binary64`
73×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	143	10
2	2278	10

Stop Event

1×	node limit

Counts

1 → 233

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

827×	`associate-/l*_binary64`
531×	`fma-def_binary64`
454×	`cancel-sign-sub-inv_binary64`
412×	`associate-/r/_binary64`
334×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	414
1	109	408
2	348	366
3	1439	324

Stop Event

1×	node limit

Counts

257 → 247

prune212.0ms (5.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	245	3	248

Error

Counts

248 → 3

Alt Table

Status	Error	Program
	0.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x y)) (neg.f64 (.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) (.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) (cbrt.f64 (/.f64 y (+.f64 x y))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) (cbrt.f64 (/.f64 y (+.f64 x y)))) (.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) (*.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) (cbrt.f64 (/.f64 y (+.f64 x y)))))))
▶	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	35.6b	(+.f64 -1 (.f64 (/.f64 x y) (-.f64 2 (.f64 2 (/.f64 x y)))))

Compiler

Compiled 12032 to 3115 computations (74.1% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series24.0ms (0.6%)

Counts

3 → 72

Calls

18 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	x	inf
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	x	0
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	x	-inf
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	y	0
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	y	-inf

rewrite75.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

498×	`fma-def_binary64`
256×	`fma-neg_binary64`
239×	`log-div_binary64`
237×	`egg-rr`
172×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	175	24
2	3034	24

Stop Event

1×	node limit

Counts

3 → 237

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
454×	`associate-/r/_binary64`
270×	`distribute-neg-frac_binary64`
225×	`distribute-rgt-neg-in_binary64`
221×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1290
1	179	1284
2	545	1095
3	2347	1008

Stop Event

1×	node limit

Counts

309 → 275

prune209.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	273	2	275
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	275	3	278

Error

Counts

278 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	35.6b	(fma.f64 2 (*.f64 (-.f64 1 (/.f64 x y)) (/.f64 x y)) -1)
▶	0.0b	(+.f64 (/.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2) (/.f64 y (+.f64 x y))))

Compiler

Compiled 5798 to 1540 computations (73.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
✓	0.2b	(pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2)
✓	7.7b	(cbrt.f64 (/.f64 y (+.f64 x y)))
✓	28.8b	(fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2) (/.f64 y (+.f64 x y)))

series1.2s (30.9%)

Counts

3 → 48

Calls

18 calls:

465.0ms	(fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2) (/.f64 y (+.f64 x y)))	y	inf
437.0ms	(fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2) (/.f64 y (+.f64 x y)))	x	0
186.0ms	(fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2) (/.f64 y (+.f64 x y)))	y	-inf
43.0ms	(pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2)	y	-inf
29.0ms	(cbrt.f64 (/.f64 y (+.f64 x y)))	y	-inf

rewrite53.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`log-prod_binary64`
209×	`fma-def_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`
150×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	53
1	221	37
2	2961	37

Stop Event

1×	node limit

Counts

3 → 109

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-/l*_binary64`
692×	`fma-def_binary64`
311×	`cancel-sign-sub-inv_binary64`
184×	`fma-neg_binary64`
164×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1257
1	458	1210
2	1884	1090

Stop Event

1×	node limit

Counts

157 → 152

prune344.0ms (8.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	462	0	462
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	462	3	465

Error

Counts

465 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
▶	35.6b	(fma.f64 2 (*.f64 (-.f64 1 (/.f64 x y)) (/.f64 x y)) -1)
✓	0.0b	(+.f64 (/.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2) (/.f64 y (+.f64 x y))))

Compiler

Compiled 25151 to 6487 computations (74.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 1 (/.f64 x y)) (/.f64 x y))

series14.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

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

rewrite43.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`log1p-expm1-u_binary64`
810×	`expm1-log1p-u_binary64`
343×	`prod-diff_binary64`
76×	`add-sqr-sqrt_binary64`
71×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	151	13
2	2096	13

Stop Event

1×	node limit

Counts

1 → 42

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

625×	`associate-/l*_binary64`
382×	`associate-/r*_binary64`
329×	`associate-/l/_binary64`
278×	`associate-l_binary64`
268×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	336
1	24	336
2	51	336
3	155	318
4	753	300
5	4678	300

Stop Event

1×	node limit

Counts

66 → 47

prune30.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	47	3	50

Error

Counts

50 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
✓	35.6b	(fma.f64 2 (*.f64 (-.f64 1 (/.f64 x y)) (/.f64 x y)) -1)
✓	0.0b	(+.f64 (/.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 y (+.f64 x y)))) (pow.f64 (cbrt.f64 (/.f64 y (+.f64 x y))) 2) (/.f64 y (+.f64 x y))))

Compiler

Compiled 882 to 499 computations (43.4% saved)

regimes460.0ms (11.7%)

Accuracy

Total 0.0b remaining (53.8%)

Threshold costs 0.0b (53.8%)

Counts

165 → 1

Compiler

Compiled 14456 to 6745 computations (53.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	10	16
2	17	16
3	21	16
4	24	16
5	25	16

Stop Event

1×

saturated

end54.0ms (1.4%)

Stop Event

1×

done

Compiler

Compiled 84 to 39 computations (53.6% saved)

Details

analyze56.0ms (1.4%)

sample730.0ms (18.5%)

preprocess67.0ms (1.7%)

simplify55.0ms (1.4%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite108.0ms (2.7%)

simplify30.0ms (0.8%)

prune212.0ms (5.4%)

localize5.0ms (0.1%)

series24.0ms (0.6%)

rewrite75.0ms (1.9%)

simplify45.0ms (1.1%)

prune209.0ms (5.3%)

localize11.0ms (0.3%)

series1.2s (30.9%)

rewrite53.0ms (1.3%)

simplify42.0ms (1.1%)

prune344.0ms (8.7%)

localize6.0ms (0.1%)

series14.0ms (0.4%)

rewrite43.0ms (1.1%)

simplify35.0ms (0.9%)

prune30.0ms (0.8%)

regimes460.0ms (11.7%)

simplify2.0ms (0.1%)

end54.0ms (1.4%)

Profiling