Details

analyze93.0ms (3.2%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample929.0ms (32.2%)

Results

898.0ms	8256×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	49	11
4	63	11
5	67	11
6	65	11

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.2b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

rewrite70.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

571×	`log1p-expm1-u_binary64`
571×	`expm1-log1p-u_binary64`
303×	`log-prod_binary64`
302×	`fma-def_binary64`
121×	`expm1-udef_binary64`

Counts

1 → 30

Calls

1 calls:

69.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	140	11
2	1507	11
3	4903	11
4	5114	11
0	0	0
1	0	0

simplify149.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

1238×	`sqr-pow_binary64`
688×	`fabs-mul_binary64`
666×	`cube-prod_binary64`
611×	`associate-l_binary64`
532×	`pow-sqr_binary64`

Counts

54 → 36

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	231
1	20	231
2	33	231
3	61	231
4	130	231
5	322	231
6	1004	231
7	1111	231
8	1273	231
9	1486	231
10	1757	231
11	2105	231
12	2536	231
13	2980	231
14	3730	231
15	4019	231
16	4362	231
17	4495	231
18	4546	231
19	4574	231
20	5448	231

prune27.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Error

0.0b

Counts

38 → 5

Alt Table

Status	Error	Program
	38.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 y 3) (.f64 x x)) 3))
	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	1.1b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) 3)
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
▶	0.2b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 582 to 334 computations (42.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	0.2b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

series23.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

8.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
7.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite93.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

752×	`fma-def_binary64`
308×	`fma-neg_binary64`
239×	`egg-rr`
173×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`

Counts

3 → 239

Calls

3 calls:

69.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
69.0ms	(+.f64 (.f64 x x) (.f64 y y))
69.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	42
1	190	30
2	2639	30
3	5021	30
0	0	0
1	0	0

simplify178.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

1078×	`sqr-pow_binary64`
786×	`cube-prod_binary64`
770×	`fabs-mul_binary64`
484×	`unswap-sqr_binary64`
392×	`pow-sqr_binary64`

Counts

311 → 251

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	666
1	27	630
2	48	630
3	86	630
4	185	630
5	457	630
6	673	630
7	1140	630
8	1207	630
9	1399	630
10	1604	630
11	1894	630
12	2170	630
13	2589	630
14	3220	630
15	3532	630
16	3884	630
17	4038	630
18	4106	630
19	4148	630
20	4945	630
21	4917	630

prune160.0ms (5.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	249	7	256

Error

0.0b

Counts

256 → 7

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))
	38.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 y 3) (.f64 x x)) 3))
	0.2b	(fma.f64 y y (pow.f64 (hypot.f64 y (hypot.f64 x y)) 2))
	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	1.1b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) 3)
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	30.3b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) y) (.f64 x x)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 4798 to 2035 computations (57.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 x y) 2)
✓	0.1b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))

series84.0ms (2.9%)

Counts

2 → 48

Calls

2 calls:

43.0ms	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))
40.0ms	(pow.f64 (hypot.f64 x y) 2)

rewrite45.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

754×	`prod-diff_binary64`
679×	`log1p-expm1-u_binary64`
679×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`

Counts

2 → 46

Calls

2 calls:

44.0ms	(pow.f64 (hypot.f64 x y) 2)
44.0ms	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	171	20
2	1752	20
3	5439	20
0	0	0
1	0	0

simplify161.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1238×	`sqr-pow_binary64`
688×	`fabs-mul_binary64`
666×	`cube-prod_binary64`
611×	`associate-l_binary64`
532×	`pow-sqr_binary64`

Counts

94 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	435
1	22	399
2	37	399
3	65	399
4	138	399
5	334	399
6	1024	399
7	1159	399
8	1321	399
9	1534	399
10	1805	399
11	2151	399
12	2582	399
13	3022	399
14	3772	399
15	4061	399
16	4404	399
17	4537	399
18	4588	399
19	4616	399
20	5490	399

prune38.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	55	7	62

Error

0.0b

Counts

62 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))
	38.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 y 3) (.f64 x x)) 3))
▶	0.2b	(fma.f64 y y (pow.f64 (hypot.f64 y (hypot.f64 x y)) 2))
	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	1.1b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) 3)
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	30.3b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) y) (.f64 x x)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 912 to 396 computations (56.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 y (hypot.f64 x y))
✓	0.1b	(fma.f64 y y (pow.f64 (hypot.f64 y (hypot.f64 x y)) 2))
✓	0.3b	(pow.f64 (hypot.f64 y (hypot.f64 x y)) 2)

series208.0ms (7.2%)

Counts

3 → 72

Calls

3 calls:

97.0ms	(fma.f64 y y (pow.f64 (hypot.f64 y (hypot.f64 x y)) 2))
92.0ms	(pow.f64 (hypot.f64 y (hypot.f64 x y)) 2)
19.0ms	(hypot.f64 y (hypot.f64 x y))

rewrite101.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

632×	`log1p-expm1-u_binary64`
632×	`expm1-log1p-u_binary64`
179×	`prod-diff_binary64`
178×	`fma-udef_binary64`
136×	`expm1-udef_binary64`

Counts

3 → 87

Calls

3 calls:

99.0ms	(hypot.f64 y (hypot.f64 x y))
99.0ms	(fma.f64 y y (pow.f64 (hypot.f64 y (hypot.f64 x y)) 2))
99.0ms	(pow.f64 (hypot.f64 y (hypot.f64 x y)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	31
1	163	30
2	1657	30
3	4922	30
4	4930	30
5	4954	30
0	0	0
1	0	0

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-neg_binary64`
611×	`times-frac_binary64`
333×	`unswap-sqr_binary64`
250×	`associate-/l*_binary64`
239×	`associate-/r*_binary64`

Counts

159 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1139
1	221	1095
2	664	1065
3	3623	1065
4	5068	1065

prune96.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	131	6	137

Error

0.0b

Counts

137 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (+.f64 y y) (pow.f64 (hypot.f64 x y) 2))
	38.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 y 3) (.f64 x x)) 3))
✓	0.2b	(fma.f64 y y (pow.f64 (hypot.f64 y (hypot.f64 x y)) 2))
	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	0.5b	(fma.f64 y y (+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 2) 2)) (pow.f64 x 2)))
	1.1b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) 3)

Compiler

Compiled 2287 to 1130 computations (50.6% saved)

regimes235.0ms (8.2%)

Accuracy

Total 0.0b remaining (84.2%)

Threshold costs 0.0b (84.2%)

Counts

47 → 1

Compiler

Compiled 3473 to 2206 computations (36.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	8	14

end92.0ms (3.2%)

Compiler: Compiled 103 to 68 computations (34% saved)

Details

analyze93.0ms (3.2%)

sample929.0ms (32.2%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series7.0ms (0.2%)

rewrite70.0ms (2.4%)

simplify149.0ms (5.2%)

prune27.0ms (0.9%)

localize6.0ms (0.2%)

series23.0ms (0.8%)

rewrite93.0ms (3.2%)

simplify178.0ms (6.2%)

prune160.0ms (5.6%)

localize7.0ms (0.2%)

series84.0ms (2.9%)

rewrite45.0ms (1.6%)

simplify161.0ms (5.6%)

prune38.0ms (1.3%)

localize6.0ms (0.2%)

series208.0ms (7.2%)

rewrite101.0ms (3.5%)

simplify59.0ms (2%)

prune96.0ms (3.3%)

regimes235.0ms (8.2%)

simplify2.0ms (0.1%)

end92.0ms (3.2%)

Profiling