Details

analyze40.0ms (1.1%)

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
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample806.0ms (22.4%)

Results

714.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify68.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
382×	`times-frac_binary64`
357×	`div-sub_binary64`
168×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	28	10
5	51	10
6	74	10
7	104	10
8	154	10
9	319	10
10	479	10
11	806	10
12	1050	10
13	1216	10
14	1316	10
15	1330	10
16	1350	10
17	1350	10
18	1250	10

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))

series8.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 47

Calls

1 calls:

5.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

simplify81.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
387×	`distribute-rgt-in_binary64`
223×	`fma-def_binary64`
161×	`associate-/l*_binary64`

Counts

71 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1282
1	280	1222
2	785	1160
3	2516	1148
4	4566	1139
5	5172	1139

prune35.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	5	58

Error

Counts

58 → 5

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (/.f64 x y) (-.f64 -2 (*.f64 2 (/.f64 x y))) -1)
	0.2b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 x y)))
▶	0.0b	(/.f64 1 (/.f64 (-.f64 x y) (+.f64 x y)))
	34.5b	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (sqrt.f64 (+.f64 x y)) (-.f64 x y)))
	30.7b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) (fma.f64 2 (pow.f64 (/.f64 y x) 3) 1))

Compiler

Compiled 997 to 351 computations (64.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 (-.f64 x y) (+.f64 x y))
8.0ms	(/.f64 1 (/.f64 (-.f64 x y) (+.f64 x y)))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

178×	`times-frac_binary64`
174×	`*-un-lft-identity_binary64`
122×	`add-sqr-sqrt_binary64`
80×	`add-cube-cbrt_binary64`
30×	`associate-/r*_binary64`

Counts

2 → 178

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 (-.f64 x y) (+.f64 x y)))
6.0ms	(/.f64 (-.f64 x y) (+.f64 x y))

simplify155.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-neg_binary64`
368×	`fma-def_binary64`
310×	`times-frac_binary64`
267×	`distribute-rgt-in_binary64`
239×	`associate-/l*_binary64`

Counts

226 → 204

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	4590
1	441	4267
2	1315	4104
3	4286	4086
4	4976	4086
5	4961	4086

prune120.0ms (3.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	205	4	209

Error

Counts

209 → 4

Alt Table

Status	Error	Program
	34.5b	(/.f64 1 (/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 x y))) (sqrt.f64 (+.f64 x y))))
▶	0.0b	(/.f64 1 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))
	0.0b	(/.f64 (/.f64 1 (-.f64 x y)) (/.f64 1 (+.f64 x y)))
	30.7b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) (fma.f64 2 (pow.f64 (/.f64 y x) 3) 1))

Compiler

Compiled 4069 to 1318 computations (67.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series47.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

16.0ms	(/.f64 1 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))
15.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
8.0ms	(/.f64 y (+.f64 x y))
8.0ms	(/.f64 x (+.f64 x y))

rewrite145.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

722×	`*-un-lft-identity_binary64`
611×	`times-frac_binary64`
418×	`add-sqr-sqrt_binary64`
358×	`add-cube-cbrt_binary64`
324×	`prod-diff_binary64`

Counts

4 → 552

Calls

4 calls:

26.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
20.0ms	(/.f64 1 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))
5.0ms	(/.f64 y (+.f64 x y))
3.0ms	(/.f64 x (+.f64 x y))

simplify453.0ms (12.6%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-neg_binary64`
261×	`distribute-rgt-in_binary64`
248×	`unsub-neg_binary64`
243×	`sub-neg_binary64`
210×	`fma-udef_binary64`

Counts

648 → 577

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	519	28160
1	1191	18347
2	2830	13892
3	4716	13879
4	4809	13879

prune342.0ms (9.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	576	1	577
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	577	4	581

Error

Counts

581 → 4

Alt Table

Status	Error	Program
	34.5b	(/.f64 1 (/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 x y))) (sqrt.f64 (+.f64 x y))))
✓	0.0b	(/.f64 1 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))
▶	0.0b	(cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)))
	30.7b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) (fma.f64 2 (pow.f64 (/.f64 y x) 3) 1))

Compiler

Compiled 22763 to 5133 computations (77.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)
	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
✓	0.0b	(/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))
✓	0.0b	(cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)))

series44.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

15.0ms	(cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)))
15.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)
14.0ms	(/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))

rewrite122.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

668×	`times-frac_binary64`
577×	`*-un-lft-identity_binary64`
417×	`add-sqr-sqrt_binary64`
289×	`add-cube-cbrt_binary64`
208×	`cube-prod_binary64`

Counts

3 → 527

Calls

3 calls:

16.0ms	(/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))
16.0ms	(cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)))
7.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)

simplify366.0ms (10.2%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
360×	`unswap-sqr_binary64`
273×	`log-prod_binary64`
164×	`associate-/r*_binary64`
155×	`log-div_binary64`

Counts

599 → 358

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	17314
1	790	15414
2	2629	14893
3	4506	14893
4	5106	14893

prune353.0ms (9.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	416	0	416
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	416	4	420

Error

Counts

420 → 4

Alt Table

Status	Error	Program
	34.5b	(/.f64 1 (/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 x y))) (sqrt.f64 (+.f64 x y))))
✓	0.0b	(/.f64 1 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))
✓	0.0b	(cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)))
	30.7b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) (fma.f64 2 (pow.f64 (/.f64 y x) 3) 1))

Compiler

Compiled 10023 to 4563 computations (54.5% saved)

regimes252.0ms (7%)

Accuracy

Total 0.0b remaining (62.8%)

Threshold costs 0.0b (62.8%)

Counts

103 → 1

Compiler

Compiled 4126 to 2832 computations (31.4% 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	9	19
1	14	19
2	20	19
3	24	19
4	27	19
5	28	19
6	27	19

end66.0ms (1.8%)

Compiler: Compiled 97 to 56 computations (42.3% saved)

Details

analyze40.0ms (1.1%)

sample806.0ms (22.4%)

simplify68.0ms (1.9%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify81.0ms (2.3%)

prune35.0ms (1%)

localize5.0ms (0.1%)

series19.0ms (0.5%)

rewrite35.0ms (1%)

simplify155.0ms (4.3%)

prune120.0ms (3.3%)

localize6.0ms (0.2%)

series47.0ms (1.3%)

rewrite145.0ms (4%)

simplify453.0ms (12.6%)

prune342.0ms (9.5%)

localize7.0ms (0.2%)

series44.0ms (1.2%)

rewrite122.0ms (3.4%)

simplify366.0ms (10.2%)

prune353.0ms (9.8%)

regimes252.0ms (7%)

simplify2.0ms (0.1%)

end66.0ms (1.8%)

Profiling