Details

analyze577.0ms (6.5%)

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)

sample688.0ms (7.8%)

Algorithm

1×

intervals

Results

10.0ms	36×	body	2048	valid
10.0ms	167×	body	128	valid
6.0ms	27×	body	1024	valid
4.0ms	11×	body	4096	valid
2.0ms	10×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	12×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
205×	`fma-def_binary64`
183×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	54	20
3	115	20
4	179	20
5	291	20
6	417	20
7	528	20
8	602	20
9	854	20
10	1802	20
11	1043	20
12	1027	20
13	1035	20
14	1043	20
15	1043	20
16	1101	20
17	1137	20
18	1139	20
19	1151	20
20	1046	20

prune2.0ms (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

35.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.7b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	22.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series265.0ms (3%)

Counts

4 → 96

Calls

4 calls:

137.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
75.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
41.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
11.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite126.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
61×	`prod-diff_binary64`
60×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 176

Calls

4 calls:

85.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
12.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify190.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
181×	`unswap-sqr_binary64`
169×	`sub-neg_binary64`
135×	`associate-r_binary64`

Counts

272 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	7693
1	779	6304
2	2682	5750
3	4584	5750
4	4974	5750

prune154.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	282	10	292
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	282	11	293

Error

5.0b

Counts

293 → 11

Alt Table

Status	Error	Program
	42.4b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	33.4b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	38.0b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	34.6b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
	42.1b	(/.f64 (*.f64 -2 b_2) a)
✓	35.7b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	58.2b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	53.8b	(fma.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b_2 7)) -5/128 (fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b_2 5)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b_2 3)) -1/8))))
	40.3b	(*.f64 -1/2 (/.f64 c b_2))
	35.8b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
▶	33.0b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))

Compiler

Compiled 9108 to 2040 computations (77.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
✓	0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
✓	0.6b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	14.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.1s (11.9%)

Counts

4 → 42

Calls

4 calls:

655.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
224.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
154.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
18.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`*-un-lft-identity_binary64`
162×	`times-frac_binary64`
139×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
34×	`distribute-lft-out--_binary64`

Counts

4 → 244

Calls

4 calls:

9.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
6.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
5.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
2.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify257.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
401×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
186×	`sub-neg_binary64`
154×	`distribute-frac-neg_binary64`

Counts

286 → 331

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	9712
1	794	8164
2	2705	7612
3	4798	7608
4	4906	7608

prune201.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	326	5	331
Fresh	6	3	9
Picked	1	0	1
Done	0	1	1
Total	333	9	342

Error

0.0b

Counts

342 → 9

Alt Table

Status	Error	Program
	40.3b	(*.f64 -1/2 (/.f64 c b_2))
	45.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
	46.3b	(/.f64 1 (fma.f64 (/.f64 (.f64 a (neg.f64 (.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (fma.f64 1/16 (/.f64 (.f64 a (.f64 (.f64 c a) (.f64 c a))) (pow.f64 b_2 5)) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))))
	38.0b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
▶	33.0b	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))
	42.1b	(/.f64 (*.f64 -2 b_2) a)
	48.0b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))) (sqrt.f64 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))))
✓	35.7b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	48.4b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))

Compiler

Compiled 10497 to 2690 computations (74.4% saved)

localize9.0ms (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)
✓	0.2b	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))
	0.6b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
	14.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series360.0ms (4.1%)

Counts

2 → 28

Calls

2 calls:

246.0ms	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))
114.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`prod-diff_binary64`
59×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`
34×	`distribute-lft-in_binary64`

Counts

2 → 122

Calls

2 calls:

14.0ms	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))
0.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify196.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
422×	`fma-neg_binary64`
245×	`distribute-rgt-in_binary64`
209×	`cancel-sign-sub-inv_binary64`
180×	`distribute-rgt-neg-out_binary64`

Counts

150 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	295	5466
1	646	4347
2	2107	3332
3	4541	3330
4	4978	3330
5	4994	3330
6	4883	3330

prune165.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	302	9	311

Error

0.0b

Counts

311 → 9

Alt Table

Status	Error	Program
	46.3b	(/.f64 1 (fma.f64 (/.f64 (.f64 a (neg.f64 (.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (fma.f64 1/16 (/.f64 (.f64 a (.f64 (.f64 c a) (.f64 c a))) (pow.f64 b_2 5)) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))))
▶	38.0b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	45.6b	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)))
	48.3b	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)))
	42.1b	(/.f64 (*.f64 -2 b_2) a)
	48.0b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))))) (sqrt.f64 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))))
✓	35.7b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	48.4b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	40.3b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 11254 to 2850 computations (74.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	3.1b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
✓	7.3b	(/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	14.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.1s (12.3%)

Counts

3 → 36

Calls

3 calls:

490.0ms

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

453.0ms

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

148.0ms

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

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 125

Calls

3 calls:

8.0ms

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

5.0ms

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

3.0ms

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

simplify181.0ms (2%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
390×	`cancel-sign-sub-inv_binary64`
251×	`fma-neg_binary64`
247×	`times-frac_binary64`
196×	`associate-/l*_binary64`

Counts

161 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	5674
1	872	4918
2	3266	4799
3	4807	4797
4	4966	4797
5	4909	4797

prune104.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	257	7	264

Error

0.0b

Counts

264 → 7

Alt Table

Status	Error	Program
	45.6b	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)))
	48.3b	(.f64 (/.f64 1 a) (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)))
	42.1b	(/.f64 (*.f64 -2 b_2) a)
✓	35.7b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	48.4b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	40.3b	(*.f64 -1/2 (/.f64 c b_2))
	33.3b	(.f64 1 (/.f64 c (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))

Compiler

Compiled 7379 to 1705 computations (76.9% saved)

regimes1.5s (16.9%)

Accuracy

Total 9.2b remaining (98.1%)

Threshold costs 0b (0%)

Counts

97 → 4

Compiler

Compiled 8880 to 5342 computations (39.8% saved)

bsearch99.0ms (1.1%)

Steps

Iters	Range		Point
9	693562986953.8666	274594520810878270.0	1003851693548.0198
11	-2.406580852722053e-303	7.446169914578951e-289	2.6030463307926315e-305
8	-4.5760233018562114e-51	-9.652306198456256e-54	-2.0523858676494354e-52

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	75
1	53	75
2	67	75
3	81	75
4	88	75
5	91	75
6	92	75
7	91	75

end1.0ms (0%)

Compiler: Compiled 53 to 29 computations (45.3% saved)

sample1.4s (16%)

Algorithm

1×

intervals

Results

306.0ms	1116×	body	2048	valid
289.0ms	5199×	body	128	valid
161.0ms	756×	body	1024	valid
131.0ms	410×	body	4096	valid
62.0ms	365×	body	512	valid
46.0ms	784×	body	128	nan
16.0ms	154×	body	256	valid
14.0ms	247×	body	128	invalid

Compiler

Compiled 175 to 115 computations (34.3% saved)

Details

analyze577.0ms (6.5%)

sample688.0ms (7.8%)

simplify82.0ms (0.9%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series265.0ms (3%)

rewrite126.0ms (1.4%)

simplify190.0ms (2.1%)

prune154.0ms (1.7%)

localize10.0ms (0.1%)

series1.1s (11.9%)

rewrite50.0ms (0.6%)

simplify257.0ms (2.9%)

prune201.0ms (2.3%)

localize9.0ms (0.1%)

series360.0ms (4.1%)

rewrite34.0ms (0.4%)

simplify196.0ms (2.2%)

prune165.0ms (1.9%)

localize9.0ms (0.1%)

series1.1s (12.3%)

rewrite29.0ms (0.3%)

simplify181.0ms (2%)

prune104.0ms (1.2%)

regimes1.5s (16.9%)

bsearch99.0ms (1.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.4s (16%)

Profiling