Details

analyze27.0ms (0.5%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.2s (23%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 36 to 24 computations (33.3% saved)

preprocess13.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

4×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	76
1	28	76
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	13	19

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (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

34.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.6b	(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))

Compiler

Compiled 62 to 36 computations (41.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3)
✓	32.1b	(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))

series111.0ms (2.2%)

Counts

2 → 72

Calls

18 calls:

15.0ms	(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))	y	-inf
12.0ms	(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))	x	-inf
11.0ms	(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))	y	0
11.0ms	(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))	z	inf
11.0ms	(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))	x	inf

rewrite46.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

833×	`log1p-expm1-u_binary64`
833×	`expm1-log1p-u_binary64`
108×	`add-sqr-sqrt_binary64`
103×	`add-cbrt-cube_binary64`
102×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	212	25
2	2229	25

Stop Event

1×	node limit

Counts

2 → 37

simplify631.0ms (12.4%)

Algorithm

1×	egg-herbie

Rules

1695×	`sqr-pow_binary64`
687×	`pow-sqr_binary64`
90×	`cube-mult_binary64`
90×	`unpow3_binary64`
87×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	307	3360
1	444	3222
2	503	3222
3	551	3222
4	612	3222
5	683	3222
6	759	3222
7	845	3222
8	936	3222
9	1037	3222
10	1143	3222
11	1259	3222
12	1380	3222
13	1511	3222
14	1647	3222
15	1793	3222
16	1944	3222
17	2105	3222
18	2271	3222
19	2447	3222
20	2489	3222
21	2527	3222
22	2527	3222
23	2673	3222
24	2853	3222
25	3050	3222
26	3252	3222
27	3464	3222
28	3681	3222
29	3908	3222
30	4140	3222
31	4382	3222
32	4394	3222
33	4400	3222
34	4400	3222
35	4644	3222
36	4895	3222

Stop Event

1×	node limit

Counts

109 → 117

prune133.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	3	118

Error

Counts

118 → 3

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))
	18.4b	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))
	19.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))

Compiler

Compiled 4265 to 3113 computations (27% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)
✓	0.0b	(hypot.f64 (hypot.f64 x y) z)
✓	0.4b	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))

series159.0ms (3.1%)

Counts

3 → 96

Calls

24 calls:

16.0ms	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))	x	inf
11.0ms	(hypot.f64 (hypot.f64 x y) z)	z	inf
11.0ms	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))	x	-inf
11.0ms	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))	y	inf
10.0ms	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))	y	0

rewrite49.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log1p-expm1-u_binary64`
655×	`expm1-log1p-u_binary64`
201×	`log-prod_binary64`
160×	`log-pow_binary64`
155×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	170	23
2	1738	23

Stop Event

1×	node limit

Counts

3 → 61

simplify858.0ms (16.9%)

Algorithm

1×	egg-herbie

Rules

1596×	`sqr-pow_binary64`
645×	`pow-sqr_binary64`
106×	`fma-def_binary64`
87×	`cube-mult_binary64`
87×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	430	5260
1	595	4996
2	658	4996
3	713	4996
4	774	4996
5	845	4996
6	921	4996
7	1007	4996
8	1098	4996
9	1199	4996
10	1305	4996
11	1421	4996
12	1542	4996
13	1673	4996
14	1809	4996
15	1955	4996
16	2106	4996
17	2267	4996
18	2433	4996
19	2609	4996
20	2651	4996
21	2689	4996
22	2689	4996
23	2835	4996
24	3015	4996
25	3212	4996
26	3414	4996
27	3626	4996
28	3843	4996
29	4070	4996
30	4302	4996
31	4544	4996
32	4556	4996
33	4562	4996
34	4562	4996
35	4806	4996

Stop Event

1×	node limit

Counts

157 → 217

prune224.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	217	3	220

Error

Counts

220 → 3

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))
▶	18.4b	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))
	19.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))

Compiler

Compiled 7963 to 5583 computations (29.9% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 z x)
✓	0.4b	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))

series31.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(hypot.f64 z x)	x	inf
4.0ms	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))	x	-inf
3.0ms	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))	z	inf
2.0ms	(hypot.f64 z x)	x	0
2.0ms	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))	z	-inf

rewrite38.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

504×	`log1p-expm1-u_binary64`
504×	`expm1-log1p-u_binary64`
183×	`unpow-prod-down_binary64`
164×	`pow2_binary64`
156×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	132	13
2	1333	13

Stop Event

1×	node limit

Counts

2 → 41

simplify400.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

1736×	`sqr-pow_binary64`
832×	`pow-sqr_binary64`
78×	`cube-prod_binary64`
78×	`cube-mult_binary64`
78×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	1244
1	144	1244
2	177	1244
3	205	1244
4	241	1244
5	284	1244
6	330	1244
7	383	1244
8	439	1244
9	502	1244
10	568	1244
11	641	1244
12	717	1244
13	800	1244
14	886	1244
15	979	1244
16	1075	1244
17	1178	1244
18	1284	1244
19	1397	1244
20	1513	1244
21	1636	1244
22	1762	1244
23	1895	1244
24	2031	1244
25	2174	1244
26	2320	1244
27	2328	1244
28	2332	1244
29	2332	1244
30	2483	1244
31	2635	1244
32	2798	1244
33	2964	1244
34	3137	1244
35	3313	1244
36	3496	1244
37	3682	1244
38	3875	1244
39	4071	1244
40	4120	1244
41	4124	1244
42	4124	1244
43	4319	1244
44	4522	1244
45	4732	1244
46	4949	1244

Stop Event

1×	node limit

Counts

89 → 97

prune60.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Error

Counts

100 → 3

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))
✓	18.4b	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))
▶	19.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))

Compiler

Compiled 1702 to 1209 computations (29% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))

series20.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

5.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	z	inf
3.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	y	-inf
3.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	z	-inf
3.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	y	inf
3.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	z	0

rewrite34.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

504×	`log1p-expm1-u_binary64`
504×	`expm1-log1p-u_binary64`
183×	`unpow-prod-down_binary64`
164×	`pow2_binary64`
156×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	132	9
2	1335	9

Stop Event

1×	node limit

Counts

1 → 18

simplify322.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

1736×	`sqr-pow_binary64`
832×	`pow-sqr_binary64`
78×	`cube-prod_binary64`
78×	`cube-mult_binary64`
78×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	772
1	129	772
2	158	772
3	186	772
4	222	772
5	265	772
6	311	772
7	364	772
8	420	772
9	483	772
10	549	772
11	622	772
12	698	772
13	781	772
14	867	772
15	960	772
16	1056	772
17	1159	772
18	1265	772
19	1378	772
20	1494	772
21	1617	772
22	1743	772
23	1876	772
24	2012	772
25	2155	772
26	2301	772
27	2309	772
28	2313	772
29	2313	772
30	2464	772
31	2616	772
32	2779	772
33	2945	772
34	3118	772
35	3294	772
36	3477	772
37	3663	772
38	3856	772
39	4052	772
40	4101	772
41	4105	772
42	4105	772
43	4300	772
44	4503	772
45	4713	772
46	4930	772

Stop Event

1×	node limit

Counts

42 → 59

prune39.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	59	3	62

Error

Counts

62 → 3

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (hypot.f64 (hypot.f64 x y) z) (sqrt.f64 3))
✓	18.4b	(*.f64 (hypot.f64 z x) (sqrt.f64 1/3))
✓	19.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))

Compiler

Compiled 1227 to 942 computations (23.2% saved)

regimes637.0ms (12.5%)

Accuracy

Total 0.4b remaining (97.9%)

Threshold costs 0.4b (97.9%)

Counts

43 → 1

Compiler

Compiled 5807 to 4519 computations (22.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12

Stop Event

1×

saturated

end52.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 51 to 38 computations (25.5% saved)

Details

analyze27.0ms (0.5%)

sample1.2s (23%)

preprocess13.0ms (0.2%)

simplify4.0ms (0.1%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

series111.0ms (2.2%)

rewrite46.0ms (0.9%)

simplify631.0ms (12.4%)

prune133.0ms (2.6%)

localize6.0ms (0.1%)

series159.0ms (3.1%)

rewrite49.0ms (1%)

simplify858.0ms (16.9%)

prune224.0ms (4.4%)

localize4.0ms (0.1%)

series31.0ms (0.6%)

rewrite38.0ms (0.8%)

simplify400.0ms (7.9%)

prune60.0ms (1.2%)

localize6.0ms (0.1%)

series20.0ms (0.4%)

rewrite34.0ms (0.7%)

simplify322.0ms (6.3%)

prune39.0ms (0.8%)

regimes637.0ms (12.5%)

simplify2.0ms (0%)

end52.0ms (1%)

Profiling