Details

analyze436.0ms (15.8%)

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
0%	99.9%	0.1%	5
9.4%	90.5%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
37.8%	60.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
56.8%	36.2%	7%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample106.0ms (3.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify130.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1119×	`div-sub_binary64`
816×	`fma-def_binary64`
804×	`fma-neg_binary64`
517×	`neg-mul-1_binary64`
483×	`neg-sub0_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	27	10
3	57	10
4	111	10
5	180	10
6	312	10
7	977	10
8	3166	10
9	3725	10
10	4150	10
11	4786	10
12	4803	10
13	4958	10
14	5387	10

prune3.0ms (0.1%)

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

11.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.7b	(/.f64 (*.f64 x (-.f64 y z)) y)

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	11.1b	(/.f64 (*.f64 x (-.f64 y z)) y)

series23.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

16.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
6.0ms	(*.f64 x (-.f64 y z))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 75

Calls

2 calls:

7.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
6.0ms	(*.f64 x (-.f64 y z))

simplify94.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-neg_binary64`
321×	`div-sub_binary64`
313×	`associate-*l/_binary64`
290×	`associate-/r*_binary64`
263×	`fma-def_binary64`

Counts

147 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1568
1	298	1439
2	1158	1383
3	3774	1383
4	4927	1383
5	5098	1383

prune117.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Error

0.0b

Counts

109 → 7

Alt Table

Status	Error	Program
	12.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 x (-.f64 y z)) y)) (cbrt.f64 (/.f64 (.f64 x (-.f64 y z)) y))) (cbrt.f64 (/.f64 (*.f64 x (-.f64 y z)) y)))
▶	2.3b	(/.f64 x (/.f64 y (-.f64 y z)))
	11.8b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
	11.7b	(/.f64 1 (/.f64 y (*.f64 x (-.f64 y z))))
	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
	31.8b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (-.f64 y z) (sqrt.f64 y)))
	8.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 y z) (cbrt.f64 y)))

Compiler

Compiled 1843 to 541 computations (70.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 y z))
✓	2.2b	(/.f64 x (/.f64 y (-.f64 y z)))

series23.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

12.0ms	(/.f64 x (/.f64 y (-.f64 y z)))
9.0ms	(/.f64 y (-.f64 y z))

rewrite24.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
102×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

2 → 143

Calls

2 calls:

7.0ms	(/.f64 x (/.f64 y (-.f64 y z)))
6.0ms	(/.f64 y (-.f64 y z))

simplify152.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-def_binary64`
516×	`associate-/r/_binary64`
497×	`times-frac_binary64`
463×	`associate-/l*_binary64`
459×	`associate-/l/_binary64`

Counts

203 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	3761
1	540	3647
2	1917	3540
3	4751	3528
4	5354	3528

prune124.0ms (4.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	211	6	217

Error

Counts

217 → 6

Alt Table

Status	Error	Program
	35.0b	(*.f64 (/.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 y)) (/.f64 x (/.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 y z)))))
	11.3b	(*.f64 (/.f64 x y) (-.f64 y z))
	11.8b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
	11.7b	(/.f64 1 (/.f64 y (*.f64 x (-.f64 y z))))
▶	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
	31.8b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (-.f64 y z) (sqrt.f64 y)))

Compiler

Compiled 3695 to 883 computations (76.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) y)
✓	2.7b	(*.f64 x (/.f64 (-.f64 y z) y))

series17.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

12.0ms	(*.f64 x (/.f64 (-.f64 y z) y))
5.0ms	(/.f64 (-.f64 y z) y)

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

2 → 80

Calls

2 calls:

9.0ms	(*.f64 x (/.f64 (-.f64 y z) y))
5.0ms	(/.f64 (-.f64 y z) y)

simplify110.0ms (4%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-def_binary64`
513×	`associate-/r/_binary64`
290×	`associate-l_binary64`
276×	`associate-*l/_binary64`
268×	`associate-*r/_binary64`

Counts

140 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1631
1	275	1534
2	871	1532
3	2610	1532
4	4832	1532
5	4977	1532

prune57.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	116	5	121

Error

Counts

121 → 5

Alt Table

Status	Error	Program
	14.4b	(.f64 (.f64 x (sqrt.f64 (/.f64 (-.f64 y z) y))) (sqrt.f64 (/.f64 (-.f64 y z) y)))
▶	11.3b	(*.f64 (/.f64 x y) (-.f64 y z))
	11.8b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
✓	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
	31.8b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (-.f64 y z) (sqrt.f64 y)))

Compiler

Compiled 1690 to 473 computations (72% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	11.0b	(*.f64 (/.f64 x y) (-.f64 y z))

series14.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(*.f64 (/.f64 x y) (-.f64 y z))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`associate-l_binary64`

Counts

1 → 66

Calls

1 calls:

8.0ms

(*.f64 (/.f64 x y) (-.f64 y z))

simplify96.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

911×	`times-frac_binary64`
318×	`associate-/r*_binary64`
313×	`associate-/l*_binary64`
302×	`fma-def_binary64`
274×	`associate-*l/_binary64`

Counts

102 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	1410
1	331	1308
2	1050	1254
3	4692	1254
4	5207	1254

prune57.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	94	5	99

Error

Counts

99 → 5

Alt Table

Status	Error	Program
	14.4b	(.f64 (.f64 x (sqrt.f64 (/.f64 (-.f64 y z) y))) (sqrt.f64 (/.f64 (-.f64 y z) y)))
✓	11.3b	(*.f64 (/.f64 x y) (-.f64 y z))
	11.8b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
✓	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
	31.8b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (-.f64 y z) (sqrt.f64 y)))

Compiler

Compiled 1710 to 412 computations (75.9% saved)

regimes466.0ms (16.9%)

Accuracy

Total 1.6b remaining (98.8%)

Threshold costs 0b (0%)

Counts

73 → 3

Compiler

Compiled 4090 to 2410 computations (41.1% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 10 to 6 computations (40% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	64
1	32	64
2	41	64
3	52	64
4	59	64
5	62	64
6	63	64
7	62	64

end1.0ms (0%)

Compiler: Compiled 46 to 20 computations (56.5% saved)

sample629.0ms (22.8%)

Algorithm

1×

intervals

Results

267.0ms	8000×	body	128	valid
34.0ms	739×	body	128	invalid

Compiler

Compiled 124 to 66 computations (46.8% saved)

Details

analyze436.0ms (15.8%)

sample106.0ms (3.8%)

simplify130.0ms (4.7%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series23.0ms (0.8%)

rewrite19.0ms (0.7%)

simplify94.0ms (3.4%)

prune117.0ms (4.3%)

localize5.0ms (0.2%)

series23.0ms (0.8%)

rewrite24.0ms (0.9%)

simplify152.0ms (5.5%)

prune124.0ms (4.5%)

localize5.0ms (0.2%)

series17.0ms (0.6%)

rewrite19.0ms (0.7%)

simplify110.0ms (4%)

prune57.0ms (2.1%)

localize5.0ms (0.2%)

series14.0ms (0.5%)

rewrite12.0ms (0.4%)

simplify96.0ms (3.5%)

prune57.0ms (2.1%)

regimes466.0ms (16.9%)

bsearch2.0ms (0.1%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample629.0ms (22.8%)

Profiling