Details

analyze6.0ms (0.3%)

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)

sample1.1s (62.2%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify26.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	58	17
5	82	17
6	117	17
7	189	17
8	356	17
9	577	17
10	789	17
11	1134	17
12	1524	17
13	1940	17
14	2181	17

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 47 to 39 computations (17% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series8.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

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

rewrite74.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

913×	`log1p-expm1-u_binary64`
913×	`expm1-log1p-u_binary64`
311×	`prod-diff_binary64`
161×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	177	36
2	2408	36

Stop Event

1×	node limit

Counts

3 → 161

Calls

3 calls:

70.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
70.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
70.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify32.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
444×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
262×	`associate-/l/_binary64`
194×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	494
1	189	468
2	609	456
3	2374	394

Stop Event

1×	node limit

Counts

185 → 187

prune146.0ms (8.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	1	188

Error

Counts

188 → 1

Alt Table

Status	Error	Program
▶	0b	(*.f64 2 (atan.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1))))

Compiler

Compiled 6007 to 4034 computations (32.8% saved)

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

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

rewrite57.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

468×	`log-prod_binary64`
186×	`prod-diff_binary64`
178×	`fma-def_binary64`
176×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	51
1	215	46
2	2753	46

Stop Event

1×	node limit

Counts

4 → 146

Calls

4 calls:

54.0ms	(atan.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1)))
54.0ms	(pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1)
54.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))
54.0ms	(sqrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1))

simplify35.0ms (2%)

Algorithm

1×	egg-herbie

Rules

530×	`cancel-sign-sub-inv_binary64`
446×	`fma-neg_binary64`
246×	`fma-def_binary64`
232×	`sub-neg_binary64`
190×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	813
1	251	766
2	819	752
3	3012	695

Stop Event

1×	node limit

Counts

194 → 185

prune114.0ms (6.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	1	186

Error

Counts

186 → 1

Alt Table

Status	Error	Program
✓	0b	(*.f64 2 (atan.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1))))

Compiler

Compiled 3350 to 2807 computations (16.2% saved)

regimes102.0ms (5.7%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

22 → 1

Compiler

Compiled 1577 to 1347 computations (14.6% saved)

simplify2.0ms (0.1%)

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	12	20
1	18	20
2	21	20
3	23	20
4	24	20

Stop Event

1×

saturated

end42.0ms (2.4%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

Details

analyze6.0ms (0.3%)

sample1.1s (62.2%)

simplify26.0ms (1.4%)

prune2.0ms (0.1%)

localize7.0ms (0.4%)

series8.0ms (0.4%)

rewrite74.0ms (4.2%)

simplify32.0ms (1.8%)

prune146.0ms (8.2%)

localize8.0ms (0.5%)

series10.0ms (0.6%)

rewrite57.0ms (3.2%)

simplify35.0ms (2%)

prune114.0ms (6.4%)

regimes102.0ms (5.7%)

simplify2.0ms (0.1%)

end42.0ms (2.4%)

Profiling