Details

analyze852.0ms (9.1%)

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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample437.0ms (4.7%)

Algorithm

1×

intervals

Results

11.0ms	33×	body	2048	valid
10.0ms	174×	body	128	valid
4.0ms	20×	body	1024	valid
4.0ms	11×	body	4096	valid
2.0ms	32×	body	128	nan
2.0ms	11×	body	512	valid
1.0ms	7×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
379×	`associate-/l*_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
224×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	39	18
3	69	18
4	107	18
5	178	18
6	279	18
7	382	18
8	547	18
9	587	18
10	855	18
11	1247	18
12	1117	18
13	1035	18
14	1043	18
15	1051	18
16	1077	18
17	1093	18
18	1129	18
19	1131	18
20	1143	18
21	1050	18

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.8b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series189.0ms (2%)

Counts

4 → 96

Calls

4 calls:

79.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
57.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
42.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
10.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
19×	`prod-diff_binary64`

Counts

4 → 120

Calls

4 calls:

8.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify265.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
364×	`cancel-sign-sub-inv_binary64`
248×	`distribute-rgt-neg-in_binary64`
220×	`distribute-lft-neg-in_binary64`
172×	`distribute-rgt-in_binary64`

Counts

216 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5492
1	683	4712
2	2484	4515
3	4521	4514
4	4915	4514
5	4990	4514
6	5000	4514
7	4999	4514
8	4932	4514

prune150.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	226	11	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	227	11	238

Error

5.6b

Counts

238 → 11

Alt Table

Status	Error	Program
	39.1b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	56.5b	(/.f64 (-.f64 b_2 b_2) a)
▶	33.8b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	47.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	45.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	42.1b	(*.f64 -1/2 (/.f64 c b_2))
	33.9b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	41.5b	(*.f64 -2 (/.f64 b_2 a))
	34.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	33.9b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

Compiler

Compiled 5913 to 1694 computations (71.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
✓	0.3b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
✓	1.0b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	14.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series570.0ms (6.1%)

Counts

4 → 38

Calls

4 calls:

210.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
197.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
146.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
18.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
9×	`prod-diff_binary64`

Counts

4 → 98

Calls

4 calls:

4.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
0.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
405×	`fma-neg_binary64`
351×	`cancel-sign-sub-inv_binary64`
265×	`div-sub_binary64`
202×	`associate-/l/_binary64`

Counts

136 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	3637
1	595	3108
2	1974	2972
3	4571	2968
4	5093	2968

prune238.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	177	9	186

Error

0.1b

Counts

186 → 9

Alt Table

Status	Error	Program
	47.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	45.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	42.1b	(*.f64 -1/2 (/.f64 c b_2))
	33.9b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	43.0b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	49.6b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	34.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
▶	33.9b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

Compiler

Compiled 4497 to 1398 computations (68.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
✓	0.3b	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
	1.0b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	14.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series679.0ms (7.2%)

Counts

2 → 24

Calls

2 calls:

438.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
241.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

rewrite30.0ms (0.3%)

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 → 149

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
4.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

simplify143.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-/l*_binary64`
605×	`associate-/r*_binary64`
347×	`fma-def_binary64`
338×	`associate-/r/_binary64`
162×	`associate-/l/_binary64`

Counts

173 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	5915
1	561	5467
2	1768	5322
3	5166	5322

prune168.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	326	2	328
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	328	9	337

Error

0.1b

Counts

337 → 9

Alt Table

Status	Error	Program
	47.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
▶	33.9b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	43.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	42.1b	(*.f64 -1/2 (/.f64 c b_2))
	33.9b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	43.0b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	49.6b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	34.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 9198 to 2541 computations (72.4% saved)

localize65.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))
✓	0.3b	(/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
	1.0b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	14.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series861.0ms (9.2%)

Counts

2 → 24

Calls

2 calls:

439.0ms	(.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))
422.0ms	(/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

2 → 89

Calls

2 calls:

8.0ms	(.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))
5.0ms	(/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-/l*_binary64`
426×	`associate-/r*_binary64`
397×	`associate-r_binary64`
344×	`associate-l_binary64`
311×	`fma-neg_binary64`

Counts

113 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	3043
1	448	2714
2	1364	2673
3	4857	2669
4	5011	2669

prune134.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	228	10	238

Error

0.1b

Counts

238 → 10

Alt Table

Status	Error	Program
	47.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
✓	33.9b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	43.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	42.1b	(*.f64 -1/2 (/.f64 c b_2))
	33.9b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	43.0b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	49.6b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	34.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	49.7b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))))

Compiler

Compiled 6405 to 2455 computations (61.7% saved)

regimes2.6s (27.9%)

Accuracy

Total 10.2b remaining (98.1%)

Threshold costs 0b (0%)

Counts

161 → 3

Compiler

Compiled 12436 to 7498 computations (39.7% saved)

bsearch51.0ms (0.5%)

Steps

Iters	Range		Point
8	3.4649656629941637e-71	1.4121860845682094e-68	4.586808464503111e-71
6	-6.949406021534192e+80	-1.6616722534479078e+80	-3.322551845096585e+80

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-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	23	47
1	33	47
2	48	47
3	58	47
4	65	47
5	67	47
6	67	47

end1.0ms (0%)

Compiler: Compiled 35 to 21 computations (40% saved)

sample1.5s (16.4%)

Algorithm

1×

intervals

Results

320.0ms	1102×	body	2048	valid
315.0ms	5225×	body	128	valid
159.0ms	694×	body	1024	valid
149.0ms	418×	body	4096	valid
63.0ms	366×	body	512	valid
49.0ms	765×	body	128	nan
21.0ms	195×	body	256	valid
16.0ms	264×	body	128	invalid

Compiler

Compiled 228 to 144 computations (36.8% saved)

Details

analyze852.0ms (9.1%)

sample437.0ms (4.7%)

simplify85.0ms (0.9%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series189.0ms (2%)

rewrite30.0ms (0.3%)

simplify265.0ms (2.8%)

prune150.0ms (1.6%)

localize8.0ms (0.1%)

series570.0ms (6.1%)

rewrite14.0ms (0.2%)

simplify117.0ms (1.2%)

prune238.0ms (2.5%)

localize9.0ms (0.1%)

series679.0ms (7.2%)

rewrite30.0ms (0.3%)

simplify143.0ms (1.5%)

prune168.0ms (1.8%)

localize65.0ms (0.7%)

series861.0ms (9.2%)

rewrite22.0ms (0.2%)

simplify105.0ms (1.1%)

prune134.0ms (1.4%)

regimes2.6s (27.9%)

bsearch51.0ms (0.5%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.5s (16.4%)

Profiling