Details

analyze610.0ms (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
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
34.7%	55.4%	9.9%	9
36.1%	51.1%	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)

sample2.4s (27.9%)

Results

738.0ms	5326×	body	128	valid
516.0ms	1128×	body	2048	valid
302.0ms	802×	body	1024	valid
230.0ms	425×	body	4096	valid
144.0ms	1114×	body	128	invalid
116.0ms	416×	body	512	valid
33.0ms	159×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify86.0ms (1%)

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

34.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.6b	(/.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
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series171.0ms (2%)

Counts

4 → 96

Calls

4 calls:

70.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
50.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
39.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
12.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite28.0ms (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:

9.0ms	(/.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)
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify266.0ms (3.1%)

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	5568
1	683	4769
2	2484	4515
3	4521	4514
4	4915	4514
5	4990	4514
6	5000	4514
7	4999	4514
8	4932	4514

prune255.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	225	12	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	226	12	238

Error

4.1b

Counts

238 → 12

Alt Table

Status	Error	Program
	31.7b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	35.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 a)))
	39.5b	(*.f64 -1/2 (/.f64 c b_2))
	56.3b	(/.f64 (-.f64 b_2 b_2) a)
	31.8b	(.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))
	44.9b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	43.3b	(/.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)
	46.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
▶	31.7b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	44.7b	(.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)))
	46.0b	(/.f64 (*.f64 -2 b_2) a)
	32.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a))) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))

Compiler

Compiled 6047 to 1720 computations (71.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
✓	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	11.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series367.0ms (4.2%)

Counts

3 → 24

Calls

3 calls:

203.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
144.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
19.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 88

Calls

3 calls:

5.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
4.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify96.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-def_binary64`
428×	`fma-neg_binary64`
291×	`cancel-sign-sub-inv_binary64`
277×	`div-sub_binary64`
219×	`associate-/r/_binary64`

Counts

112 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3125
1	530	2608
2	1783	2484
3	4376	2480
4	5049	2480

prune132.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	143	11	154

Error

0.1b

Counts

154 → 11

Alt Table

Status	Error	Program
▶	31.7b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	35.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 a)))
	31.8b	(.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))
	44.9b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	32.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a))) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	45.4b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	47.0b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	46.2b	(/.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2)) a)
	39.5b	(*.f64 -1/2 (/.f64 c b_2))
✓	31.7b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	44.7b	(.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)))

Compiler

Compiled 3862 to 1140 computations (70.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	11.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series619.0ms (7.1%)

Counts

2 → 24

Calls

2 calls:

407.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
211.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

rewrite32.0ms (0.4%)

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:

10.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
7.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

simplify132.0ms (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 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	5993
1	561	5467
2	1768	5322
3	5166	5322

prune168.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	293	4	297
Fresh	3	6	9
Picked	0	1	1
Done	1	0	1
Total	297	11	308

Error

0.0b

Counts

308 → 11

Alt Table

Status	Error	Program
	39.5b	(*.f64 -1/2 (/.f64 c b_2))
	44.9b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (.f64 2 (/.f64 (.f64 a b_2) (neg.f64 (*.f64 c a))))))
	31.8b	(.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))
	44.9b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	47.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
▶	31.7b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	47.0b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	31.8b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	46.2b	(/.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2)) a)
✓	31.7b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	45.4b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)

Compiler

Compiled 8417 to 2424 computations (71.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	11.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series206.0ms (2.4%)

Counts

1 → 12

Calls

1 calls:

206.0ms

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

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 69

Calls

1 calls:

8.0ms

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

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-/l*_binary64`
489×	`associate-/r*_binary64`
447×	`fma-def_binary64`
216×	`associate-*l/_binary64`
191×	`distribute-rgt-in_binary64`

Counts

81 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2317
1	469	2032
2	1462	1897
3	4681	1895
4	4962	1895

prune115.0ms (1.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	194	12	206

Error

0.0b

Counts

206 → 12

Alt Table

Status	Error	Program
	39.5b	(*.f64 -1/2 (/.f64 c b_2))
	44.9b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (.f64 2 (/.f64 (.f64 a b_2) (neg.f64 (*.f64 c a))))))
	31.8b	(.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))
	44.9b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	47.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
✓	31.7b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	31.8b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	46.2b	(/.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 b_2 -2)) a)
✓	31.7b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	47.0b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))
	42.9b	(-.f64 (/.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) a) (/.f64 b_2 a))
	45.4b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)

Compiler

Compiled 5341 to 1726 computations (67.7% saved)

regimes2.6s (30.1%)

Accuracy

Total 9.5b remaining (97.7%)

Threshold costs 0b (0%)

Counts

158 → 3

Compiler

Compiled 13936 to 7778 computations (44.2% saved)

bsearch73.0ms (0.8%)

Steps

Iters	Range		Point
9	1.3254205640108585e-89	1.0528149194740619e-82	4.1451903108450355e-85
8	-6.049269811617561e+72	-2.8564673789894883e+69	-5.667728209619793e+72

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	28	54
1	42	54
2	54	54
3	62	54
4	67	54
5	68	54
6	67	54

end142.0ms (1.6%)

Compiler: Compiled 274 to 175 computations (36.1% saved)

Details

analyze610.0ms (7%)

sample2.4s (27.9%)

simplify86.0ms (1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series171.0ms (2%)

rewrite28.0ms (0.3%)

simplify266.0ms (3.1%)

prune255.0ms (2.9%)

localize8.0ms (0.1%)

series367.0ms (4.2%)

rewrite16.0ms (0.2%)

simplify96.0ms (1.1%)

prune132.0ms (1.5%)

localize9.0ms (0.1%)

series619.0ms (7.1%)

rewrite32.0ms (0.4%)

simplify132.0ms (1.5%)

prune168.0ms (1.9%)

localize8.0ms (0.1%)

series206.0ms (2.4%)

rewrite18.0ms (0.2%)

simplify82.0ms (0.9%)

prune115.0ms (1.3%)

regimes2.6s (30.1%)

bsearch73.0ms (0.8%)

simplify3.0ms (0%)

end142.0ms (1.6%)

Profiling