Details

analyze394.0ms (17.7%)

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)

sample94.0ms (4.2%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	27×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify114.0ms (5.1%)

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

prune1.0ms (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

11.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.6b	(/.f64 (*.f64 x (-.f64 y z)) y)

Compiler

Compiled 30 to 18 computations (40% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)

series21.0ms (1%)

Counts

2 → 72

Calls

2 calls:

11.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
10.0ms	(*.f64 x (-.f64 y z))

rewrite16.0ms (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:

6.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
5.0ms	(*.f64 x (-.f64 y z))

simplify88.0ms (3.9%)

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

prune59.0ms (2.7%)

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
	35.4b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 y z))) y)
	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
	11.7b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
	11.7b	(/.f64 1 (/.f64 y (*.f64 x (-.f64 y z))))
▶	2.4b	(*.f64 x (/.f64 (-.f64 y z) y))
	37.4b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (-.f64 y z) (sqrt.f64 y)))
	9.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 y z) (cbrt.f64 y)))

Compiler

Compiled 1813 to 539 computations (70.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) y)
✓	2.3b	(*.f64 x (/.f64 (-.f64 y z) y))

series18.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(*.f64 x (/.f64 (-.f64 y z) y))
7.0ms	(/.f64 (-.f64 y z) y)

rewrite16.0ms (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:

7.0ms	(*.f64 x (/.f64 (-.f64 y z) y))
4.0ms	(/.f64 (-.f64 y z) y)

simplify82.0ms (3.7%)

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

prune60.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	115	7	122

Error

Counts

122 → 7

Alt Table

Status	Error	Program
	35.4b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 y z))) y)
▶	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
	11.7b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
	11.7b	(/.f64 1 (/.f64 y (*.f64 x (-.f64 y z))))
✓	2.4b	(*.f64 x (/.f64 (-.f64 y z) y))
	37.4b	(.f64 (.f64 x (/.f64 1 (sqrt.f64 y))) (/.f64 (-.f64 y z) (sqrt.f64 y)))
	9.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 y z) (cbrt.f64 y)))

Compiler

Compiled 1744 to 511 computations (70.7% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 y z))
✓	2.3b	(/.f64 x (/.f64 y (-.f64 y z)))

series20.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(/.f64 x (/.f64 y (-.f64 y z)))
8.0ms	(/.f64 y (-.f64 y z))

rewrite27.0ms (1.2%)

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:

9.0ms	(/.f64 y (-.f64 y z))
6.0ms	(/.f64 x (/.f64 y (-.f64 y z)))

simplify122.0ms (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

prune87.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	211	6	217

Error

Counts

217 → 6

Alt Table

Status	Error	Program
▶	11.4b	(*.f64 (/.f64 x y) (-.f64 y z))
✓	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
	11.7b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
	11.7b	(/.f64 1 (/.f64 y (*.f64 x (-.f64 y z))))
✓	2.4b	(*.f64 x (/.f64 (-.f64 y z) y))
	11.5b	(/.f64 (/.f64 x y) (/.f64 1 (-.f64 y z)))

Compiler

Compiled 3651 to 863 computations (76.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	11.2b	(*.f64 (/.f64 x y) (-.f64 y z))

series11.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

11.0ms

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

rewrite16.0ms (0.7%)

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:

12.0ms

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

simplify67.0ms (3%)

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

prune38.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	95	5	100

Error

Counts

100 → 5

Alt Table

Status	Error	Program
	4.3b	(+.f64 x (neg.f64 (/.f64 (*.f64 z x) y)))
✓	11.4b	(*.f64 (/.f64 x y) (-.f64 y z))
✓	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
	11.7b	(/.f64 1 (/.f64 y (*.f64 x (-.f64 y z))))
	11.5b	(/.f64 (/.f64 x y) (/.f64 1 (-.f64 y z)))

Compiler

Compiled 1701 to 411 computations (75.8% saved)

regimes259.0ms (11.6%)

Accuracy

Total 1.6b remaining (99%)

Threshold costs 0b (0%)

Counts

42 → 3

Compiler

Compiled 2474 to 1374 computations (44.5% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	60
1	40	60
2	56	60
3	65	60
4	70	60
5	71	60
6	70	60

end1.0ms (0%)

Compiler: Compiled 44 to 21 computations (52.3% saved)

sample591.0ms (26.6%)

Algorithm

1×

intervals

Results

265.0ms	8000×	body	128	valid
23.0ms	736×	body	128	invalid

Compiler

Compiled 113 to 66 computations (41.6% saved)

Details

analyze394.0ms (17.7%)

sample94.0ms (4.2%)

simplify114.0ms (5.1%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series21.0ms (1%)

rewrite16.0ms (0.7%)

simplify88.0ms (3.9%)

prune59.0ms (2.7%)

localize4.0ms (0.2%)

series18.0ms (0.8%)

rewrite16.0ms (0.7%)

simplify82.0ms (3.7%)

prune60.0ms (2.7%)

localize7.0ms (0.3%)

series20.0ms (0.9%)

rewrite27.0ms (1.2%)

simplify122.0ms (5.5%)

prune87.0ms (3.9%)

localize4.0ms (0.2%)

series11.0ms (0.5%)

rewrite16.0ms (0.7%)

simplify67.0ms (3%)

prune38.0ms (1.7%)

regimes259.0ms (11.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample591.0ms (26.6%)

Profiling