Details

analyze465.0ms (9.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.7s (33.5%)

Results

765.0ms	6275×	body	128	valid
347.0ms	669×	body	2048	valid
332.0ms	567×	body	4096	valid
170.0ms	410×	body	1024	valid
68.0ms	230×	body	512	valid
22.0ms	105×	body	256	valid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess14.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	30
1	23	30
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`hypot-def_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	15	15

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

16.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	38.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (hypot.f64 re im) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.3b	(sqrt.f64 (*.f64 2 (+.f64 (hypot.f64 re im) re)))
✓	1.3b	(+.f64 (hypot.f64 re im) re)

series48.0ms (0.9%)

Counts

3 → 56

Calls

18 calls:

6.0ms	(sqrt.f64 (*.f64 2 (+.f64 (hypot.f64 re im) re)))	im	0
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 (hypot.f64 re im) re)))	re	-inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 (hypot.f64 re im) re)))	im	-inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 (hypot.f64 re im) re)))	im	inf
3.0ms	(hypot.f64 re im)	re	0

rewrite36.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log1p-expm1-u_binary64`
655×	`expm1-log1p-u_binary64`
198×	`log-prod_binary64`
149×	`log-pow_binary64`
146×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	159	23
2	1698	23

Stop Event

1×	node limit

Counts

3 → 68

simplify342.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

1614×	`sqr-pow_binary64`
718×	`pow-sqr_binary64`
72×	`cube-prod_binary64`
72×	`cube-mult_binary64`
72×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	138	1351
1	213	1311
2	261	1311
3	310	1311
4	359	1311
5	414	1311
6	471	1311
7	534	1311
8	601	1311
9	676	1311
10	754	1311
11	839	1311
12	927	1311
13	1022	1311
14	1120	1311
15	1225	1311
16	1333	1311
17	1448	1311
18	1566	1311
19	1691	1311
20	1819	1311
21	1954	1311
22	2092	1311
23	2237	1311
24	2385	1311
25	2540	1311
26	2548	1311
27	2552	1311
28	2552	1311
29	2708	1311
30	2869	1311
31	3037	1311
32	3212	1311
33	3390	1311
34	3575	1311
35	3763	1311
36	3958	1311
37	4156	1311
38	4361	1311
39	4408	1311
40	4412	1311
41	4412	1311
42	4615	1311
43	4823	1311

Stop Event

1×	node limit

Counts

124 → 136

prune93.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	130	8	138

Error

9.2b

Counts

138 → 8

Alt Table

Status	Error	Program
	17.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
	18.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
▶	16.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2)))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))
	56.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	21.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (exp.f64 (log.f64 (hypot.f64 re im))) re))))

Compiler

Compiled 3017 to 2095 computations (30.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (+.f64 (hypot.f64 re im) re))
✓	0.4b	(*.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2))
	1.3b	(+.f64 (hypot.f64 re im) re)

series50.0ms (1%)

Counts

2 → 16

Calls

12 calls:

10.0ms	(sqrt.f64 (+.f64 (hypot.f64 re im) re))	im	0
6.0ms	(*.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2))	re	-inf
6.0ms	(*.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2))	im	0
5.0ms	(*.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2))	im	-inf
5.0ms	(*.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2))	im	inf

rewrite32.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

708×	`log1p-expm1-u_binary64`
708×	`expm1-log1p-u_binary64`
165×	`log-pow_binary64`
158×	`expm1-udef_binary64`
158×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	178	21
2	1868	21

Stop Event

1×	node limit

Counts

2 → 38

simplify238.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1637×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
93×	`cube-mult_binary64`
93×	`unpow3_binary64`
90×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	120	800
1	184	760
2	229	760
3	275	760
4	332	760
5	397	760
6	468	760
7	547	760
8	633	760
9	728	760
10	830	760
11	940	760
12	1057	760
13	1182	760
14	1314	760
15	1454	760
16	1601	760
17	1756	760
18	1918	760
19	2088	760
20	2265	760
21	2450	760
22	2462	760
23	2468	760
24	2468	760
25	2657	760
26	2851	760
27	3058	760
28	3273	760
29	3495	760
30	3725	760
31	3962	760
32	4207	760
33	4459	760
34	4471	760
35	4477	760
36	4477	760
37	4734	760
38	4995	760

Stop Event

1×	node limit

Counts

54 → 67

prune107.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	162	9	171

Error

9.2b

Counts

171 → 9

Alt Table

Status	Error	Program
▶	17.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
	18.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
	56.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.7b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 (.f64 im im) re))) (sqrt.f64 2)))
✓	16.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2)))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	21.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (exp.f64 (log.f64 (hypot.f64 re im))) re))))

Compiler

Compiled 3866 to 2755 computations (28.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(sqrt.f64 (*.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 re im)) 2)
✓	10.2b	(+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)

series58.0ms (1.1%)

Counts

3 → 40

Calls

18 calls:

7.0ms	(sqrt.f64 (*.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))	im	0
6.0ms	(pow.f64 (sqrt.f64 (hypot.f64 re im)) 2)	re	inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))	re	-inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))	im	inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))	im	-inf

rewrite35.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`log1p-expm1-u_binary64`
709×	`expm1-log1p-u_binary64`
158×	`expm1-udef_binary64`
158×	`log1p-udef_binary64`
91×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	200	23
2	1909	23

Stop Event

1×	node limit

Counts

3 → 50

simplify293.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1614×	`sqr-pow_binary64`
718×	`pow-sqr_binary64`
72×	`cube-prod_binary64`
72×	`cube-mult_binary64`
72×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	131	1021
1	200	981
2	244	981
3	294	981
4	343	981
5	398	981
6	455	981
7	518	981
8	585	981
9	660	981
10	738	981
11	823	981
12	911	981
13	1006	981
14	1104	981
15	1209	981
16	1317	981
17	1432	981
18	1550	981
19	1675	981
20	1803	981
21	1938	981
22	2076	981
23	2221	981
24	2369	981
25	2524	981
26	2532	981
27	2536	981
28	2536	981
29	2692	981
30	2853	981
31	3021	981
32	3196	981
33	3374	981
34	3559	981
35	3747	981
36	3942	981
37	4140	981
38	4345	981
39	4392	981
40	4396	981
41	4396	981
42	4599	981
43	4807	981

Stop Event

1×	node limit

Counts

90 → 105

prune101.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	151	9	160

Error

9.2b

Counts

160 → 9

Alt Table

Status	Error	Program
✓	17.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
▶	18.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
	56.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.7b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 (.f64 im im) re))) (sqrt.f64 2)))
✓	16.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2)))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	21.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (exp.f64 (log.f64 (hypot.f64 re im)))) 2) re))))

Compiler

Compiled 3455 to 2447 computations (29.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (hypot.f64 re im))
	0.0b	(hypot.f64 re im)
✓	0.3b	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)))
✓	18.3b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)

series91.0ms (1.8%)

Counts

3 → 26

Calls

18 calls:

16.0ms	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)))	im	-inf
15.0ms	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)))	im	inf
9.0ms	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)))	im	0
6.0ms	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)	im	inf
6.0ms	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re)	im	-inf

rewrite34.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`log1p-expm1-u_binary64`
636×	`expm1-log1p-u_binary64`
200×	`log-prod_binary64`
162×	`log-pow_binary64`
149×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	171	25
2	1709	25

Stop Event

1×	node limit

Counts

3 → 73

simplify273.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1690×	`sqr-pow_binary64`
686×	`pow-sqr_binary64`
72×	`cube-prod_binary64`
72×	`cube-mult_binary64`
72×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	128	807
1	192	767
2	237	767
3	285	767
4	338	767
5	396	767
6	457	767
7	524	767
8	595	767
9	674	767
10	756	767
11	845	767
12	937	767
13	1036	767
14	1138	767
15	1247	767
16	1359	767
17	1478	767
18	1600	767
19	1729	767
20	1861	767
21	2000	767
22	2142	767
23	2291	767
24	2443	767
25	2451	767
26	2455	767
27	2455	767
28	2612	767
29	2770	767
30	2939	767
31	3111	767
32	3290	767
33	3472	767
34	3661	767
35	3853	767
36	4052	767
37	4254	767
38	4463	767
39	4471	767
40	4475	767
41	4475	767
42	4685	767
43	4900	767

Stop Event

1×	node limit

Counts

99 → 116

prune151.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	246	9	255

Error

9.2b

Counts

255 → 9

Alt Table

Status	Error	Program
	56.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.7b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 (.f64 im im) re))) (sqrt.f64 2)))
✓	16.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (hypot.f64 re im) re)) (sqrt.f64 2)))
✓	17.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	21.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 re im)))) re))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	18.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (pow.f64 (pow.f64 (hypot.f64 re im) 1/4) 2) re))))

Compiler

Compiled 5959 to 3569 computations (40.1% saved)

regimes785.0ms (15.3%)

Accuracy

Total 2.8b remaining (27.2%)

Threshold costs 0b (0%)

Counts

82 → 2

Compiler

Compiled 9558 to 7185 computations (24.8% saved)

bsearch2.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(sqrt.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))

Steps

Iters	Point		Range
0.0	∈ [	0.0	,	6.948185182524366e-141	]

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	61
1	31	61

Stop Event

1×

saturated

end125.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 222 to 172 computations (22.5% saved)

Details

analyze465.0ms (9.1%)

sample1.7s (33.5%)

preprocess14.0ms (0.3%)

simplify4.0ms (0.1%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series48.0ms (0.9%)

rewrite36.0ms (0.7%)

simplify342.0ms (6.7%)

prune93.0ms (1.8%)

localize7.0ms (0.1%)

series50.0ms (1%)

rewrite32.0ms (0.6%)

simplify238.0ms (4.6%)

prune107.0ms (2.1%)

localize9.0ms (0.2%)

series58.0ms (1.1%)

rewrite35.0ms (0.7%)

simplify293.0ms (5.7%)

prune101.0ms (2%)

localize8.0ms (0.2%)

series91.0ms (1.8%)

rewrite34.0ms (0.7%)

simplify273.0ms (5.3%)

prune151.0ms (2.9%)

regimes785.0ms (15.3%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end125.0ms (2.4%)

Profiling