Details

analyze306.0ms (11.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample20.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify285.0ms (10.4%)

Algorithm

1×	egg-herbie

Rules

2074×	`distribute-lft-out--_binary64`
788×	`distribute-rgt-out--_binary64`
756×	`unsub-neg_binary64`
614×	`sub-neg_binary64`
581×	`distribute-rgt-out_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	31	20
4	45	20
5	60	20
6	96	20
7	213	20
8	364	20
9	486	20
10	1099	20
11	1877	20
12	1931	20
13	2167	20
14	2315	20
15	2313	20
16	2390	20
17	2649	20
18	3212	20
19	4204	20
20	4738	20
21	4780	20
22	4791	20
23	4788	20
24	4573	20
25	4366	20
26	4503	20
27	4563	20
28	4606	20
29	7544	20

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite185.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
31×	`sqrt-prod_binary64`
31×	`add-cube-cbrt_binary64`

Counts

4 → 117

Calls

4 calls:

28.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
23.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 2373 to 1498 computations (36.9% saved)

series60.0ms (2.2%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

11.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
10.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
9.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
9.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 721 to 592 computations (17.9% saved)

simplify152.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

437×	`distribute-rgt-neg-in_binary64`
362×	`distribute-lft-neg-in_binary64`
295×	`sub-neg_binary64`
285×	`associate-r_binary64`
285×	`associate-l_binary64`

Counts

141 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	3074
1	424	2865
2	1065	2831
3	3056	2701
4	4966	2701
5	4875	2701

prune65.0ms (2.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	2	77

Error

Counts

77 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 x)))))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Status

Error

Program

▶

0.0b

(log.f64 (*.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))

✓

0.0b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 1148 to 764 computations (33.4% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(/.f64 (sqrt.f64 1) (sqrt.f64 x))
0.5b	(.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 x))))

rewrite426.0ms (15.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

184×	`sqrt-prod_binary64`
178×	`times-frac_binary64`
159×	`add-sqr-sqrt_binary64`
155×	`*-un-lft-identity_binary64`
113×	`add-cube-cbrt_binary64`

Counts

4 → 281

Calls

4 calls:

86.0ms	(.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 x))))
8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
6.0ms	(/.f64 (sqrt.f64 1) (sqrt.f64 x))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 6818 to 3994 computations (41.4% saved)

series32.0ms (1.2%)

Error

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 x))))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
7.0ms	(/.f64 1 (sqrt.f64 x))
6.0ms	(/.f64 (sqrt.f64 1) (sqrt.f64 x))

Compiler

Compiled 475 to 363 computations (23.6% saved)

simplify254.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

562×	`times-frac_binary64`
345×	`associate-/l*_binary64`
304×	`associate-*l/_binary64`
278×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`

Counts

293 → 229

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	6491
1	459	5445
2	1285	5213
3	3297	5011
4	4595	5011
5	4959	5011

prune135.0ms (4.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	229	2	231

Error

Counts

231 → 2

Alt Table

Status	Error	Program
	0.0b	(log.f64 (.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 x)))))
	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Status

Error

Program

0.0b

(log.f64 (*.f64 (/.f64 (sqrt.f64 1) (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))

0.0b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 2859 to 1644 computations (42.5% saved)

regimes107.0ms (3.9%)

Accuracy

Total 0.0b remaining (6.9%)

Threshold costs 0.0b (6.9%)

Compiler

Compiled 1222 to 883 computations (27.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	23	32
2	29	32
3	33	32
4	35	32
5	34	32

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample692.0ms (25.2%)

Algorithm

1×

intervals

Results

426.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 73 to 52 computations (28.8% saved)

Details

analyze306.0ms (11.1%)

sample20.0ms (0.7%)

simplify285.0ms (10.4%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite185.0ms (6.7%)

series60.0ms (2.2%)

simplify152.0ms (5.5%)

prune65.0ms (2.4%)

localize13.0ms (0.5%)

rewrite426.0ms (15.5%)

series32.0ms (1.2%)

simplify254.0ms (9.2%)

prune135.0ms (4.9%)

regimes107.0ms (3.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample692.0ms (25.2%)

Profiling