Details

analyze448.0ms (14.8%)

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)

sample995.0ms (32.9%)

Results

810.0ms	8256×	body	128	valid
75.0ms	825×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify132.0ms (4.4%)

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%)

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

14.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.8b	(/.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))
✓	14.2b	(/.f64 (*.f64 x (-.f64 y z)) y)

series19.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

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

rewrite15.0ms (0.5%)

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))

simplify89.0ms (3%)

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

prune56.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Error

0.0b

Counts

109 → 6

Alt Table

Status	Error	Program
	39.2b	(/.f64 (+.f64 (.f64 y x) (.f64 (*.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z)) x)) y)
	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
	40.5b	(/.f64 (*.f64 (-.f64 y z) (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))
▶	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
	6.2b	(-.f64 x (/.f64 (*.f64 z x) y))
	36.6b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (-.f64 y z) (sqrt.f64 y)))

Compiler

Compiled 1785 to 521 computations (70.8% saved)

localize6.0ms (0.2%)

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)))

series19.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

12.0ms	(/.f64 x (/.f64 y (-.f64 y z)))
7.0ms	(/.f64 y (-.f64 y z))

rewrite29.0ms (1%)

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 x (/.f64 y (-.f64 y z)))
3.0ms	(/.f64 y (-.f64 y z))

simplify185.0ms (6.1%)

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

prune99.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	210	6	216

Error

Counts

216 → 6

Alt Table

Status	Error	Program
	6.2b	(-.f64 x (/.f64 (*.f64 z x) y))
	10.0b	(*.f64 (/.f64 x y) (-.f64 y z))
▶	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
✓	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
	14.8b	(*.f64 (/.f64 1 y) (/.f64 x (/.f64 1 (-.f64 y z))))
	34.2b	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 y z)))) (/.f64 x (/.f64 y (sqrt.f64 (-.f64 y z)))))

Compiler

Compiled 3677 to 877 computations (76.1% saved)

localize4.0ms (0.1%)

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))

series18.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

13.0ms	(*.f64 x (/.f64 (-.f64 y z) y))
5.0ms	(/.f64 (-.f64 y z) y)

rewrite16.0ms (0.5%)

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)

simplify86.0ms (2.9%)

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

prune70.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	115	6	121

Error

Counts

121 → 6

Alt Table

Status	Error	Program
	13.3b	(.f64 (.f64 x (sqrt.f64 (/.f64 (-.f64 y z) y))) (sqrt.f64 (/.f64 (-.f64 y z) y)))
✓	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
✓	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
▶	6.2b	(-.f64 x (/.f64 (*.f64 z x) y))
	14.8b	(*.f64 (/.f64 1 y) (/.f64 x (/.f64 1 (-.f64 y z))))
	34.2b	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 y z)))) (/.f64 x (/.f64 y (sqrt.f64 (-.f64 y z)))))

Compiler

Compiled 1716 to 491 computations (71.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (*.f64 z x) y))
✓	7.7b	(/.f64 (*.f64 z x) y)

series23.0ms (0.8%)

Counts

2 → 18

Calls

2 calls:

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

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`prod-diff_binary64`
20×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

2 → 69

Calls

2 calls:

4.0ms	(-.f64 x (/.f64 (*.f64 z x) y))
3.0ms	(/.f64 (*.f64 z x) y)

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
714×	`associate-/l*_binary64`
631×	`times-frac_binary64`
246×	`associate-/l/_binary64`
130×	`distribute-rgt-neg-in_binary64`

Counts

87 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1424
1	334	1197
2	1130	1008
3	4401	1008
4	4909	1008

prune64.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
✓	2.4b	(/.f64 x (/.f64 y (-.f64 y z)))
	6.2b	(-.f64 x (/.f64 1 (/.f64 y (*.f64 z x))))
✓	2.9b	(*.f64 x (/.f64 (-.f64 y z) y))
	4.0b	(-.f64 x (/.f64 z (/.f64 y x)))
	34.2b	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 y z)))) (/.f64 x (/.f64 y (sqrt.f64 (-.f64 y z)))))

Compiler

Compiled 1957 to 492 computations (74.9% saved)

regimes469.0ms (15.5%)

Accuracy

Total 2.7b remaining (99.6%)

Threshold costs 0b (0%)

Counts

82 → 3

Compiler

Compiled 5102 to 2850 computations (44.1% saved)

bsearch16.0ms (0.5%)

Steps

Iters	Range		Point
6	-8.841573028744197e-274	-1.458378164320082e-274	-3.046667818042877e-274
1	-7.369579479260475e+52	-1.729742845005892e+45	-1.096355097136844e+49

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	54
1	42	54
2	63	54
3	77	54
4	85	54
5	87	54
6	87	54

end70.0ms (2.3%)

Compiler: Compiled 140 to 80 computations (42.9% saved)

Details

analyze448.0ms (14.8%)

sample995.0ms (32.9%)

simplify132.0ms (4.4%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series19.0ms (0.6%)

rewrite15.0ms (0.5%)

simplify89.0ms (3%)

prune56.0ms (1.9%)

localize6.0ms (0.2%)

series19.0ms (0.6%)

rewrite29.0ms (1%)

simplify185.0ms (6.1%)

prune99.0ms (3.3%)

localize4.0ms (0.1%)

series18.0ms (0.6%)

rewrite16.0ms (0.5%)

simplify86.0ms (2.9%)

prune70.0ms (2.3%)

localize6.0ms (0.2%)

series23.0ms (0.8%)

rewrite12.0ms (0.4%)

simplify65.0ms (2.1%)

prune64.0ms (2.1%)

regimes469.0ms (15.5%)

bsearch16.0ms (0.5%)

simplify4.0ms (0.1%)

end70.0ms (2.3%)

Profiling