Details

analyze24.0ms (1.3%)

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)

sample1.2s (64.7%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify35.0ms (1.9%)

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

prune2.0ms (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)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite20.0ms (1.1%)

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:

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

simplify111.0ms (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

prune78.0ms (4.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

Counts

121 → 1

Alt Table

Status	Error	Program
▶	0b	(*.f64 2 (atan.f64 (sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))

Compiler

Compiled 2373 to 1934 computations (18.5% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
✓	0.0b	(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))

series8.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
3.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

rewrite13.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`sqrt-prod_binary64`

Counts

2 → 67

Calls

2 calls:

5.0ms	(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
3.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

simplify74.0ms (4%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
468×	`fma-def_binary64`
440×	`associate-l_binary64`
376×	`associate-r_binary64`
192×	`associate-/r*_binary64`

Counts

91 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	1993
1	458	1434
2	1354	1376
3	4445	1376
4	5050	1376

prune61.0ms (3.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	117	1	118

Error

Counts

118 → 1

Alt Table

Status	Error	Program
✓	0b	(*.f64 2 (atan.f64 (sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))

Compiler

Compiled 2574 to 1341 computations (47.9% saved)

regimes63.0ms (3.4%)

Accuracy

Total 0.4b remaining (97.3%)

Threshold costs 0.4b (97.3%)

Counts

12 → 1

Compiler

Compiled 852 to 725 computations (14.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	11	13
2	11	13

end138.0ms (7.5%)

Compiler: Compiled 30 to 26 computations (13.3% 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

analyze24.0ms (1.3%)

sample1.2s (64.7%)

simplify35.0ms (1.9%)

prune2.0ms (0.1%)

localize7.0ms (0.4%)

series7.0ms (0.4%)

rewrite20.0ms (1.1%)

simplify111.0ms (6%)

prune78.0ms (4.2%)

localize8.0ms (0.4%)

series8.0ms (0.4%)

rewrite13.0ms (0.7%)

simplify74.0ms (4%)

prune61.0ms (3.3%)

regimes63.0ms (3.4%)

simplify2.0ms (0.1%)

end138.0ms (7.5%)

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