Details

analyze1.6s (13.5%)

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)

sample90.0ms (0.8%)

Algorithm

1×

intervals

Results

27.0ms	45×	body	2048	valid
17.0ms	159×	body	128	valid
11.0ms	26×	body	1024	valid
9.0ms	14×	body	4096	valid
3.0ms	31×	body	128	nan
2.0ms	8×	body	512	valid
1.0ms	8×	body	128	invalid
1.0ms	4×	body	256	valid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify110.0ms (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

prune3.0ms (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

35.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.1b	(/.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)

localize17.0ms (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)
✓	0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	23.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite86.0ms (0.7%)

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:

22.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
19.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series420.0ms (3.6%)

Counts

4 → 96

Calls

4 calls:

158.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
140.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
76.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
45.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify544.0ms (4.6%)

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 → 521

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	8791
1	779	6792
2	2682	5750
3	4584	5750
4	4974	5750

prune307.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	513	8	521
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	514	8	522

Error

4.1b

Counts

522 → 8

Alt Table

Status	Error	Program
	35.2b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	38.6b	(*.f64 -1/2 (/.f64 c b_2))
	44.7b	(/.f64 (*.f64 -2 b_2) a)
	37.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	56.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
▶	32.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	33.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) a)

Compiler

Compiled 8983 to 1942 computations (78.4% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
✓	0.2b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	11.4b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
18×	`times-frac_binary64`

Counts

3 → 123

Calls

3 calls:

15.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
11.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
4.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

series674.0ms (5.7%)

Counts

3 → 28

Calls

3 calls:

360.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
282.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
31.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify258.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
451×	`fma-neg_binary64`
296×	`div-sub_binary64`
232×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`

Counts

151 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	4852
1	599	3789
2	1923	3346
3	4316	3342
4	4897	3342

prune247.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	233	3	236
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	236	8	244

Error

0.1b

Counts

244 → 8

Alt Table

Status	Error	Program
	47.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
✓	32.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	38.6b	(*.f64 -1/2 (/.f64 c b_2))
▶	32.6b	(.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (/.f64 1 a))
	44.7b	(/.f64 (*.f64 -2 b_2) a)
	37.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	46.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	33.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))

Compiler

Compiled 5344 to 1242 computations (76.8% saved)

localize55.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (/.f64 1 a))
	0.2b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
	11.4b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 45

Calls

1 calls:

21.0ms

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

series435.0ms (3.7%)

Counts

1 → 14

Calls

1 calls:

434.0ms

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

simplify137.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
469×	`fma-neg_binary64`
382×	`associate-/l*_binary64`
255×	`fma-def_binary64`
192×	`distribute-rgt-in_binary64`

Counts

59 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1762
1	393	1575
2	1240	1558
3	4698	1558
4	5012	1558

prune200.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	262	1	263
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	262	9	271

Error

0.0b

Counts

271 → 9

Alt Table

Status	Error	Program
	47.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
✓	32.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	38.6b	(*.f64 -1/2 (/.f64 c b_2))
	46.4b	(.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) (/.f64 1 a))
✓	32.6b	(.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (/.f64 1 a))
	44.7b	(/.f64 (*.f64 -2 b_2) a)
	37.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	46.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
▶	33.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))

Compiler

Compiled 6111 to 1690 computations (72.3% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
	11.4b	(sqrt.f64 (neg.f64 (*.f64 c a)))
	11.4b	(sqrt.f64 (neg.f64 (*.f64 c a)))
	11.4b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`cbrt-prod_binary64`
4×	`add-sqr-sqrt_binary64`
2×	`distribute-lft-out--_binary64`
2×	`cbrt-div_binary64`

Counts

1 → 18

Calls

1 calls:

7.0ms

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

series1.6s (13.5%)

Counts

1 → 14

Calls

1 calls:

1.6s	(cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))

simplify134.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

576×	`associate-l_binary64`
456×	`associate-/r*_binary64`
424×	`associate-/l*_binary64`
280×	`fma-def_binary64`
209×	`fma-neg_binary64`

Counts

32 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1529
1	380	1406
2	1149	1300
3	4897	1300
4	4970	1300

prune117.0ms (1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	360	9	369

Error

0.0b

Counts

369 → 9

Alt Table

Status	Error	Program
	47.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
✓	32.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	38.6b	(*.f64 -1/2 (/.f64 c b_2))
	46.4b	(.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) (/.f64 1 a))
✓	32.6b	(.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (/.f64 1 a))
	44.7b	(/.f64 (*.f64 -2 b_2) a)
	37.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	46.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
✓	33.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)))) (/.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))

Compiler

Compiled 5319 to 1344 computations (74.7% saved)

regimes1.8s (15.7%)

Accuracy

Total 10.4b remaining (97.5%)

Threshold costs 0b (0%)

Compiler

Compiled 7660 to 4020 computations (47.5% saved)

bsearch114.0ms (1%)

Steps

Iters	Range		Point
9	3.586437907391441e+43	1.9202886616587692e+49	1.8985554710420717e+49
10	-3.50355082705793e-94	-3.3267235029611844e-107	-4.195208749600831e-95

Compiler

Compiled 4 to 3 computations (25% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	46
1	43	46
2	58	46
3	73	46
4	86	46
5	89	46
6	90	46
7	87	46

end1.0ms (0%)

Compiler: Compiled 34 to 22 computations (35.3% saved)

sample2.6s (22.4%)

Algorithm

1×

intervals

Results

579.0ms	1136×	body	2048	valid
533.0ms	5245×	body	128	valid
306.0ms	729×	body	1024	valid
252.0ms	396×	body	4096	valid
98.0ms	326×	body	512	valid
77.0ms	806×	body	128	nan
35.0ms	168×	body	256	valid
25.0ms	260×	body	128	invalid

Compiler

Compiled 210 to 128 computations (39% saved)

Details

analyze1.6s (13.5%)

sample90.0ms (0.8%)

simplify110.0ms (0.9%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite86.0ms (0.7%)

series420.0ms (3.6%)

simplify544.0ms (4.6%)

prune307.0ms (2.6%)

localize17.0ms (0.1%)

rewrite49.0ms (0.4%)

series674.0ms (5.7%)

simplify258.0ms (2.2%)

prune247.0ms (2.1%)

localize55.0ms (0.5%)

rewrite29.0ms (0.2%)

series435.0ms (3.7%)

simplify137.0ms (1.2%)

prune200.0ms (1.7%)

localize26.0ms (0.2%)

rewrite10.0ms (0.1%)

series1.6s (13.5%)

simplify134.0ms (1.1%)

prune117.0ms (1%)

regimes1.8s (15.7%)

bsearch114.0ms (1%)

simplify14.0ms (0.1%)

end1.0ms (0%)

sample2.6s (22.4%)

Profiling