Details

analyze5.0ms (0.2%)

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 (35.5%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify27.0ms (0.9%)

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 (0.2%)

Local error

Found 3 expressions with local error:

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

series8.0ms (0.2%)

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))))

rewrite77.0ms (2.5%)

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:

69.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
69.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
69.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify30.0ms (1%)

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

prune209.0ms (6.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	3	188

Error

Counts

188 → 3

Alt Table

Status	Error	Program
	0.0b	(*.f64 2 (atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)))
	0.0b	(.f64 2 (atan.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))))
▶	0.0b	(*.f64 2 (atan.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))))

Compiler

Compiled 6101 to 4112 computations (32.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
2.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))
2.0ms	(atan.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))))

rewrite53.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`log-prod_binary64`
186×	`prod-diff_binary64`
174×	`fma-def_binary64`
168×	`expm1-udef_binary64`
167×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	54
1	201	48
2	2695	48

Stop Event

1×	node limit

Counts

4 → 130

Calls

4 calls:

51.0ms	(sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
51.0ms	(/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
51.0ms	(atan.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))))
51.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))

simplify38.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

472×	`cancel-sign-sub-inv_binary64`
328×	`sub-neg_binary64`
307×	`associate-+l+_binary64`
298×	`fma-neg_binary64`
287×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1015
1	259	958
2	870	947
3	3555	946

Stop Event

1×	node limit

Counts

178 → 168

prune155.0ms (5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	169	2	171

Error

Counts

171 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (atan.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (sqrt.f64 (-.f64 1 x)))))))
	0.0b	(*.f64 2 (atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)))

Compiler

Compiled 3270 to 2772 computations (15.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.6%)

Counts

4 → 32

Calls

4 calls:

6.0ms	(/.f64 1 (sqrt.f64 (-.f64 1 x)))
5.0ms	(sqrt.f64 (+.f64 1 x))
4.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (sqrt.f64 (-.f64 1 x))))
2.0ms	(atan.f64 (/.f64 1 (*.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (sqrt.f64 (-.f64 1 x))))))

rewrite55.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`log-prod_binary64`
196×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
191×	`log-pow_binary64`
190×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	242	41
2	3124	41

Stop Event

1×	node limit

Counts

4 → 113

Calls

4 calls:

53.0ms	(sqrt.f64 (+.f64 1 x))
53.0ms	(atan.f64 (/.f64 1 (*.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (sqrt.f64 (-.f64 1 x))))))
53.0ms	(/.f64 1 (sqrt.f64 (-.f64 1 x)))
53.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (sqrt.f64 (-.f64 1 x))))

simplify29.0ms (1%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-def_binary64`
230×	`distribute-neg-in_binary64`
206×	`sub-neg_binary64`
202×	`cancel-sign-sub-inv_binary64`
190×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	604
1	191	582
2	597	569
3	2440	553

Stop Event

1×	node limit

Counts

145 → 137

prune113.0ms (3.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	137	2	139

Error

Counts

139 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (atan.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (sqrt.f64 (-.f64 1 x)))))))
▶	0.0b	(*.f64 2 (atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)))

Compiler

Compiled 2750 to 2388 computations (13.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)
✓	0.0b	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
✓	0.0b	(atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3))
	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

series15.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

10.0ms	(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)
3.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
2.0ms	(atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3))

rewrite47.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

311×	`prod-diff_binary64`
194×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
184×	`fma-def_binary64`
168×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	250	39
2	3099	39

Stop Event

1×	node limit

Counts

3 → 64

Calls

3 calls:

46.0ms	(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)
46.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
46.0ms	(atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3))

simplify85.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-neg_binary64`
316×	`sub-neg_binary64`
233×	`distribute-rgt-neg-in_binary64`
226×	`distribute-neg-frac_binary64`
222×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	569
1	191	533
2	690	483
3	3033	464

Stop Event

1×	node limit

Counts

88 → 89

prune197.0ms (6.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	215	2	217

Error

Counts

217 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (atan.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (sqrt.f64 (-.f64 1 x)))))))
✓	0.0b	(*.f64 2 (atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)))

Compiler

Compiled 6964 to 4907 computations (29.5% saved)

regimes701.0ms (22.9%)

Accuracy

Total 0.0b remaining (35.2%)

Threshold costs 0.0b (35.2%)

Counts

161 → 1

Compiler

Compiled 15123 to 12692 computations (16.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	4294967295
1	21	4294967295
2	26	4294967295
3	29	4294967295
4	30	4294967295

Stop Event

1×

saturated

end66.0ms (2.2%)

Compiler: Compiled 62 to 54 computations (12.9% saved)

Details

analyze5.0ms (0.2%)

sample1.1s (35.5%)

simplify27.0ms (0.9%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite77.0ms (2.5%)

simplify30.0ms (1%)

prune209.0ms (6.8%)

localize8.0ms (0.2%)

series13.0ms (0.4%)

rewrite53.0ms (1.7%)

simplify38.0ms (1.2%)

prune155.0ms (5%)

localize9.0ms (0.3%)

series17.0ms (0.6%)

rewrite55.0ms (1.8%)

simplify29.0ms (1%)

prune113.0ms (3.7%)

localize10.0ms (0.3%)

series15.0ms (0.5%)

rewrite47.0ms (1.5%)

simplify85.0ms (2.8%)

prune197.0ms (6.4%)

regimes701.0ms (22.9%)

simplify2.0ms (0.1%)

end66.0ms (2.2%)

Profiling