Details

analyze11.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample209.0ms (8.4%)

Algorithm

1×

intervals

Results

63.0ms

256×

body

128

valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify65.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

396×	`fma-neg_binary64`
375×	`fma-def_binary64`
260×	`div-sub_binary64`
123×	`times-frac_binary64`
116×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

prune3.0ms (0.1%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize14.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series17.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
6.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite45.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64`

Counts

2 → 97

Calls

2 calls:

15.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
13.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

simplify190.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
573×	`div-sub_binary64`
247×	`associate-/r*_binary64`
244×	`sub-neg_binary64`
227×	`fma-def_binary64`

Counts

121 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2420
1	399	2303
2	1084	2291
3	3339	2286
4	4735	2286
5	5704	2286

prune160.0ms (6.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	119	2	121

Error

Counts

121 → 2

Alt Table

Status	Error	Program
▶	0.7b	(*.f64 2 (atan.f64 (-.f64 1 x)))
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 2374 to 1935 computations (18.5% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (-.f64 1 x))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(atan.f64 (-.f64 1 x))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 9

Calls

1 calls:

1.0ms

(atan.f64 (-.f64 1 x))

simplify171.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

9 → 10

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	96
1	19	83
2	25	83
3	36	83
4	48	83
5	67	83
6	95	83
7	157	83
8	335	83
9	640	83
10	644	83
11	774	83
12	928	83
13	1096	83
14	1325	83
15	1626	83
16	1974	83
17	2449	83
18	3067	83
19	3263	83
20	3437	83
21	3551	83
22	3598	83
23	3650	83
24	4528	83
25	4817	83

prune12.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	10	2	12

Error

Counts

12 → 2

Alt Table

Status	Error	Program
✓	0.7b	(*.f64 2 (atan.f64 (-.f64 1 x)))
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 126 to 108 computations (14.3% saved)

regimes61.0ms (2.4%)

Accuracy

Total 0.0b remaining (17.3%)

Threshold costs 0.0b (17.3%)

Counts

3 → 1

Compiler

Compiled 202 to 169 computations (16.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	16	17
2	20	17
3	22	17
4	23	17
5	22	17

end1.0ms (0%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

sample1.5s (60.8%)

Algorithm

1×

intervals

Results

955.0ms

8000×

body

128

valid

Compiler

Compiled 45 to 38 computations (15.6% saved)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

Details

analyze11.0ms (0.4%)

sample209.0ms (8.4%)

simplify65.0ms (2.6%)

prune3.0ms (0.1%)

localize14.0ms (0.6%)

series17.0ms (0.7%)

rewrite45.0ms (1.8%)

simplify190.0ms (7.6%)

prune160.0ms (6.4%)

localize8.0ms (0.3%)

series3.0ms (0.1%)

rewrite2.0ms (0.1%)

simplify171.0ms (6.8%)

prune12.0ms (0.5%)

regimes61.0ms (2.4%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample1.5s (60.8%)

Profiling

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17