Details

analyze280.0ms (14.4%)

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)

sample24.0ms (1.2%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify269.0ms (13.8%)

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

prune1.0ms (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)

localize9.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

rewrite49.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

23×	`*-un-lft-identity_binary64`
13×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`distribute-lft-out_binary64`
8×	`sqrt-prod_binary64`

Counts

2 → 41

Calls

2 calls:

17.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 804 to 516 computations (35.8% saved)

series22.0ms (1.1%)

Error

Counts

2 → 10

Calls

2 calls:

9.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 328 to 267 computations (18.6% saved)

simplify73.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-/l*_binary64`
361×	`div-sub_binary64`
352×	`cancel-sign-sub-inv_binary64`
255×	`associate-/r*_binary64`
215×	`associate-/l/_binary64`

Counts

51 → 32

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	877
1	233	810
2	550	807
3	1559	759
4	4315	759
5	4951	759

prune20.0ms (1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	1	33

Error

Counts

33 → 1

Alt Table

Status	Error	Program
▶	0b	(log.f64 (exp.f64 (log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))))

Compiler

Compiled 534 to 366 computations (31.5% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
5.8b	(exp.f64 (log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)))

rewrite96.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

50×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
19×	`exp-sum_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(exp.f64 (log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)))
7.0ms	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
4.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 2089 to 1447 computations (30.7% saved)

series45.0ms (2.3%)

Error

Counts

4 → 20

Calls

4 calls:

11.0ms	(exp.f64 (log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)))
8.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
7.0ms	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
6.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 737 to 624 computations (15.3% saved)

simplify126.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

587×	`prod-exp_binary64`
373×	`distribute-rgt-neg-in_binary64`
337×	`div-exp_binary64`
312×	`distribute-lft-neg-in_binary64`
302×	`associate-r_binary64`

Counts

119 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	2473
1	387	2239
2	923	2163
3	2728	2115
4	4213	2115
5	5341	2115

prune38.0ms (2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	1	78

Error

Counts

78 → 1

Alt Table

Status	Error	Program
	0b	(log.f64 (exp.f64 (log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))))

Compiler

Compiled 1071 to 763 computations (28.8% saved)

regimes85.0ms (4.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Compiler

Compiled 1192 to 898 computations (24.7% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	17	17
2	23	17
3	27	17
4	29	17
5	28	17

end0.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample793.0ms (40.8%)

Algorithm

1×

intervals

Results

554.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 42 to 32 computations (23.8% saved)

Details

analyze280.0ms (14.4%)

sample24.0ms (1.2%)

simplify269.0ms (13.8%)

prune1.0ms (0.1%)

localize9.0ms (0.5%)

rewrite49.0ms (2.5%)

series22.0ms (1.1%)

simplify73.0ms (3.8%)

prune20.0ms (1%)

localize11.0ms (0.6%)

rewrite96.0ms (4.9%)

series45.0ms (2.3%)

simplify126.0ms (6.5%)

prune38.0ms (2%)

regimes85.0ms (4.4%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample793.0ms (40.8%)

Profiling