Details

analyze805.0ms (9%)

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample39.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	174×	body	128	valid
7.0ms	29×	body	2048	valid
5.0ms	26×	body	1024	valid
4.0ms	12×	body	4096	valid
1.0ms	25×	body	128	nan
1.0ms	8×	body	512	valid
1.0ms	7×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify346.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1228×	`associate-/l*_binary64`
1150×	`div-sub_binary64`
630×	`distribute-rgt-in_binary64`
619×	`times-frac_binary64`
588×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	24
2	62	24
3	121	24
4	172	24
5	282	24
6	460	24
7	748	24
8	1084	24
9	1128	24
10	1799	24
11	2594	24
12	2001	24
13	2089	24
14	2153	24
15	2179	24
16	2431	24
17	2909	24
18	2913	24
19	2991	24
20	3053	24
21	3065	24
22	3035	24
23	3211	24
24	3211	24
25	2043	24
26	2195	24
27	2097	24
28	2107	24
29	2107	24
30	2107	24
31	2107	24
32	1834	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

33.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	33.7b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite162.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

33.4b

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 1903 to 985 computations (48.2% saved)

series225.0ms (2.5%)

Error

5.9b

Counts

4 → 70

Calls

4 calls:

60.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
49.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
47.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
39.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2904 to 2077 computations (28.5% saved)

simplify151.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

876×	`times-frac_binary64`
498×	`associate-/l*_binary64`
181×	`distribute-rgt-in_binary64`
175×	`distribute-lft-in_binary64`
172×	`cancel-sign-sub-inv_binary64`

Counts

144 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3092
1	532	2857
2	1590	2851
3	4990	2851
4	4994	2851
5	5054	2851

prune64.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Error

5.8b

Counts

93 → 8

Alt Table

Status	Error	Program
	43.3b	(/.f64 (neg.f64 b) a)
	45.7b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)))
	49.6b	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 a 2))
	42.1b	(neg.f64 (/.f64 c b))
▶	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
	33.7b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	45.6b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 b b)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (*.f64 a 2)))
	45.3b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))

Compiler

Compiled 1464 to 817 computations (44.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite111.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

28×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`

Counts

4 → 83

Calls

4 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2202 to 1153 computations (47.6% saved)

series216.0ms (2.4%)

Error

5.8b

Counts

4 → 70

Calls

4 calls:

59.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
49.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
47.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
38.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2904 to 2077 computations (28.5% saved)

simplify158.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
291×	`distribute-rgt-in_binary64`
283×	`distribute-lft-in_binary64`
161×	`cancel-sign-sub-inv_binary64`
146×	`distribute-rgt-neg-in_binary64`

Counts

153 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	3334
1	563	3103
2	1814	3097
3	4847	3097
4	4991	3097
5	4946	3097

prune56.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	91	8	99

Error

5.8b

Counts

99 → 8

Alt Table

Status	Error	Program
	43.3b	(/.f64 (neg.f64 b) a)
	45.7b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)))
	49.6b	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 a 2))
	42.1b	(neg.f64 (/.f64 c b))
✓	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
▶	33.7b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	45.6b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 b b)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (*.f64 a 2)))
	45.3b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))

Compiler

Compiled 1406 to 785 computations (44.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite400.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

693×	`times-frac_binary64`
439×	`add-sqr-sqrt_binary64`
364×	`*-un-lft-identity_binary64`
290×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`

Counts

4 → 356

Calls

4 calls:

24.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 11060 to 6512 computations (41.1% saved)

series220.0ms (2.5%)

Error

5.8b

Counts

4 → 70

Calls

4 calls:

59.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
50.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
48.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
39.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3102 to 2275 computations (26.7% saved)

simplify544.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

482×	`associate-/l/_binary64`
316×	`associate-/r/_binary64`
230×	`*-commutative_binary64`
190×	`associate-*l/_binary64`
174×	`distribute-rgt-in_binary64`

Counts

426 → 378

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	410	17504
1	945	16458
2	2988	16166
3	4896	16166
4	4996	16166
5	4936	16166

prune152.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	377	1	378
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	377	9	386

Error

5.8b

Counts

386 → 9

Alt Table

Status	Error	Program
	43.3b	(/.f64 (neg.f64 b) a)
	45.7b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)))
	49.6b	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 a 2))
▶	34.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) 2)) (/.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)) a))
	42.1b	(neg.f64 (/.f64 c b))
✓	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
✓	33.7b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	45.6b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 b b)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (*.f64 a 2)))
	45.3b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))

Compiler

Compiled 5082 to 2760 computations (45.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

8×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64`
6×	`sqrt-prod_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 54

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2279 to 1229 computations (46.1% saved)

series237.0ms (2.7%)

Error

5.8b

Counts

4 → 74

Calls

4 calls:

60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
46.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
45.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 5165 to 3541 computations (31.4% saved)

simplify145.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-l_binary64`
469×	`associate-r_binary64`
456×	`times-frac_binary64`
341×	`unswap-sqr_binary64`
191×	`associate-/r*_binary64`

Counts

128 → 80

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	2082
1	210	1992
2	673	1992
3	3773	1992
4	4860	1992
5	4978	1992
6	4939	1992

prune55.0ms (0.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	80	9	89

Error

5.8b

Counts

89 → 9

Alt Table

Status	Error	Program
	43.3b	(/.f64 (neg.f64 b) a)
	45.7b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)))
	49.6b	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 a c) b) (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)))) (.f64 a 2))
	34.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) 2)) (/.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)) a))
	42.1b	(neg.f64 (/.f64 c b))
	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
	33.7b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	45.6b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 b b)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (*.f64 a 2)))
	45.3b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))

Compiler

Compiled 1705 to 984 computations (42.3% saved)

regimes3.2s (36%)

Accuracy

Total 4.7b remaining (45.6%)

Threshold costs 0b (0%)

Compiler

Compiled 23396 to 15790 computations (32.5% saved)

bsearch62.0ms (0.7%)

Steps

Iters	Range		Point
8	1.8212929551081654e-99	1.0047263301286403e-95	9.505235373997507e-96
10	-9.396747132125144e+93	-2.688297840869266e+80	-2.6468296244054407e+91

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	58
1	42	58
2	61	58
3	79	58
4	91	58
5	96	58
6	97	58
7	96	58

end1.0ms (0%)

Compiler: Compiled 42 to 26 computations (38.1% saved)

sample1.4s (15.9%)

Algorithm

1×

intervals

Results

279.0ms	1127×	body	2048	valid
252.0ms	5194×	body	128	valid
139.0ms	745×	body	1024	valid
127.0ms	413×	body	4096	valid
50.0ms	345×	body	512	valid
33.0ms	667×	body	128	nan
20.0ms	405×	body	128	invalid
16.0ms	176×	body	256	valid

Compiler

Compiled 277 to 173 computations (37.5% saved)

Details

analyze805.0ms (9%)

sample39.0ms (0.4%)

simplify346.0ms (3.9%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite162.0ms (1.8%)

series225.0ms (2.5%)

simplify151.0ms (1.7%)

prune64.0ms (0.7%)

localize10.0ms (0.1%)

rewrite111.0ms (1.2%)

series216.0ms (2.4%)

simplify158.0ms (1.8%)

prune56.0ms (0.6%)

localize12.0ms (0.1%)

rewrite400.0ms (4.5%)

series220.0ms (2.5%)

simplify544.0ms (6.1%)

prune152.0ms (1.7%)

localize17.0ms (0.2%)

rewrite81.0ms (0.9%)

series237.0ms (2.7%)

simplify145.0ms (1.6%)

prune55.0ms (0.6%)

regimes3.2s (36%)

bsearch62.0ms (0.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.4s (15.9%)

Profiling