Details

analyze1.3s (22.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.4s (41.8%)

Results

1.1s	6217×	body	128	valid
544.0ms	826×	body	2048	valid
304.0ms	533×	body	1024	valid
278.0ms	313×	body	4096	valid
95.0ms	256×	body	512	valid
28.0ms	111×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	39	22
3	45	22
4	47	22
5	49	22
6	50	22
7	47	22

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	0.6b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	13.8b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series77.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

24.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
22.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
21.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
10.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

rewrite64.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

560×	`log-prod_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
192×	`log-pow_binary64`
169×	`prod-diff_binary64`

Counts

4 → 124

Calls

4 calls:

61.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
61.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
61.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
61.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	71
1	244	67
2	2773	67
3	5005	67
0	0	0
1	0	0

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-/l*_binary64`
565×	`fma-def_binary64`
497×	`fma-neg_binary64`
413×	`cancel-sign-sub-inv_binary64`
237×	`neg-mul-1_binary64`

Counts

220 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	2325
1	603	2253
2	1998	2139
3	4625	2133
4	4991	2133

prune181.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	233	5	238

Error

3.6b

Counts

238 → 5

Alt Table

Status	Error	Program
	53.9b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
✓	14.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.5b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
	51.0b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
▶	14.2b	(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))))

Compiler

Compiled 5246 to 3797 computations (27.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)
✓	0.7b	(expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))
✓	0.7b	(+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))))
✓	29.5b	(sqrt.f64 (.f64 p (.f64 p 4)))

series86.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

34.0ms	(expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))
33.0ms	(+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))))
17.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)
1.0ms	(sqrt.f64 (.f64 p (.f64 p 4)))

rewrite69.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

336×	`prod-diff_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`

Counts

4 → 113

Calls

4 calls:

66.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)
66.0ms	(expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))
66.0ms	(+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2))))
66.0ms	(sqrt.f64 (.f64 p (.f64 p 4)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
1	307	54
2	3462	54
3	4869	54
0	0	0
1	0	0

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

947×	`associate-/r*_binary64`
417×	`cancel-sign-sub-inv_binary64`
239×	`sub-neg_binary64`
218×	`associate-/r/_binary64`
196×	`fma-neg_binary64`

Counts

197 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	3103
1	616	2893
2	2310	2513
3	5507	2513

prune188.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	199	5	204

Error

3.6b

Counts

204 → 5

Alt Table

Status	Error	Program
	53.9b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
✓	14.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	54.5b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
▶	51.0b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
✓	14.2b	(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))))

Compiler

Compiled 5393 to 4290 computations (20.5% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
✓	0.2b	(/.f64 (*.f64 x x) p)
✓	22.8b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series40.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
9.0ms	(/.f64 (*.f64 x x) p)
5.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite56.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

761×	`log1p-expm1-u_binary64`
761×	`expm1-log1p-u_binary64`
133×	`egg-rr`
129×	`log1p-udef_binary64`
75×	`add-sqr-sqrt_binary64`

Counts

3 → 133

Calls

3 calls:

54.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
54.0ms	(/.f64 (*.f64 x x) p)
54.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
1	152	18
2	2000	18
3	5084	18
0	0	0
1	0	0

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
738×	`unswap-sqr_binary64`
718×	`times-frac_binary64`
333×	`associate-/l*_binary64`
325×	`fma-neg_binary64`

Counts

205 → 138

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	520
1	23	520
2	40	520
3	106	520
4	397	520
5	2323	520
6	3969	520
7	4320	520
8	5229	520

prune48.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	139	4	143

Error

Counts

143 → 4

Alt Table

Status	Error	Program
	54.5b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
✓	14.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	44.5b	(fabs.f64 (/.f64 p x))
✓	14.2b	(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))))

Compiler

Compiled 1513 to 689 computations (54.5% saved)

localize3.0ms (0%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
	54.5b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
✓	14.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	44.5b	(fabs.f64 (/.f64 p x))
✓	14.2b	(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (sqrt.f64 (.f64 p (.f64 p 4))))) 1/2)))))

Compiler

Compiled 56 to 40 computations (28.6% saved)

regimes874.0ms (15.4%)

Accuracy

Total 0.1b remaining (50.5%)

Threshold costs 0.1b (50.5%)

Counts

99 → 2

Compiler

Compiled 10638 to 8492 computations (20.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	50
1	28	50
2	28	50

end76.0ms (1.3%)

Compiler: Compiled 126 to 88 computations (30.2% saved)

Details

analyze1.3s (22.2%)

sample2.4s (41.8%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series77.0ms (1.4%)

rewrite64.0ms (1.1%)

simplify87.0ms (1.5%)

prune181.0ms (3.2%)

localize13.0ms (0.2%)

series86.0ms (1.5%)

rewrite69.0ms (1.2%)

simplify81.0ms (1.4%)

prune188.0ms (3.3%)

localize5.0ms (0.1%)

series40.0ms (0.7%)

rewrite56.0ms (1%)

simplify67.0ms (1.2%)

prune48.0ms (0.8%)

localize3.0ms (0%)

prune3.0ms (0.1%)

regimes874.0ms (15.4%)

bsearch3.0ms (0%)

simplify2.0ms (0%)

end76.0ms (1.3%)

Profiling