Details

analyze91.0ms (3.6%)

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)

sample979.0ms (38.8%)

Results

947.0ms	8256×	body	128	valid
1.0ms	10×	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

0.0b

Counts

3 → 2

Alt Table

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

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite73.0ms (2.9%)

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 → 29

Calls

1 calls:

72.0ms

(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

simplify152.0ms (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

53 → 35

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

prune25.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Error

0.0b

Counts

37 → 4

Alt Table

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

Compiler

Compiled 556 to 327 computations (41.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
✓	0.2b	(*.f64 3 (pow.f64 y 2))

series11.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
2.0ms	(*.f64 3 (pow.f64 y 2))

rewrite52.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

861×	`prod-diff_binary64`
805×	`expm1-log1p-u_binary64`
90×	`log1p-expm1-u_binary64`
89×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Counts

2 → 50

Calls

2 calls:

51.0ms	(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
51.0ms	(*.f64 3 (pow.f64 y 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	194	18
2	2062	18
3	4989	18
0	0	0
1	0	0

simplify135.0ms (5.4%)

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

56 → 54

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	33
1	17	33
2	28	33
3	54	33
4	119	33
5	305	33
6	975	33
7	1048	33
8	1210	33
9	1423	33
10	1694	33
11	2043	33
12	2474	33
13	2922	33
14	3672	33
15	3961	33
16	4304	33
17	4437	33
18	4488	33
19	4516	33
20	5390	33

prune59.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	53	5	58

Error

0.0b

Counts

58 → 5

Alt Table

Status	Error	Program
	0.6b	(+.f64 (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3) (pow.f64 x 2))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.2b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
▶	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
	14.1b	(+.f64 (sqrt.f64 (*.f64 9 (pow.f64 y 4))) (pow.f64 x 2))

Compiler

Compiled 866 to 510 computations (41.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

10.0ms

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

rewrite65.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

538×	`log1p-expm1-u_binary64`
538×	`expm1-log1p-u_binary64`
335×	`unpow-prod-down_binary64`
274×	`log-prod_binary64`
166×	`pow2_binary64`

Counts

1 → 36

Calls

1 calls:

64.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	139	11
2	1417	11
3	5262	11
0	0	0
1	0	0

simplify151.0ms (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

60 → 42

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

prune26.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	42	5	47

Error

0.0b

Counts

47 → 5

Alt Table

Status	Error	Program
	0.6b	(+.f64 (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3) (pow.f64 x 2))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
▶	0.2b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
	14.1b	(+.f64 (sqrt.f64 (*.f64 9 (pow.f64 y 4))) (pow.f64 x 2))

Compiler

Compiled 700 to 371 computations (47% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3))))
✓	0.2b	(.f64 y (.f64 y 3))
✓	0.2b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
✓	18.5b	(sqrt.f64 (.f64 y (.f64 y 3)))

series142.0ms (5.6%)

Counts

4 → 72

Calls

4 calls:

115.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
22.0ms	(hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3))))
3.0ms	(sqrt.f64 (.f64 y (.f64 y 3)))
2.0ms	(.f64 y (.f64 y 3))

rewrite58.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

768×	`log1p-expm1-u_binary64`
768×	`expm1-log1p-u_binary64`
191×	`prod-diff_binary64`
94×	`add-sqr-sqrt_binary64`
90×	`add-log-exp_binary64`

Counts

4 → 87

Calls

4 calls:

57.0ms	(hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3))))
57.0ms	(.f64 y (.f64 y 3))
57.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
57.0ms	(sqrt.f64 (.f64 y (.f64 y 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	204	33
2	2059	33
3	5073	33
0	0	0
1	0	0

simplify84.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

714×	`times-frac_binary64`
331×	`associate-/l*_binary64`
304×	`associate-r_binary64`
293×	`associate-/r*_binary64`
263×	`associate-l_binary64`

Counts

159 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	1351
1	211	1062
2	748	1038
3	4827	1038
4	4985	1038
5	4962	1038

prune120.0ms (4.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	122	6	128

Error

Counts

128 → 6

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3)))))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
	0.6b	(+.f64 (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3) (pow.f64 x 2))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
✓	0.2b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	14.1b	(+.f64 (sqrt.f64 (*.f64 9 (pow.f64 y 4))) (pow.f64 x 2))

Compiler

Compiled 1994 to 1490 computations (25.3% saved)

regimes157.0ms (6.2%)

Accuracy

Total 0.1b remaining (88.8%)

Threshold costs 0.1b (88.8%)

Counts

26 → 1

Compiler

Compiled 1697 to 1186 computations (30.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end85.0ms (3.4%)

Compiler: Compiled 102 to 72 computations (29.4% saved)

Details

analyze91.0ms (3.6%)

sample979.0ms (38.8%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite73.0ms (2.9%)

simplify152.0ms (6%)

prune25.0ms (1%)

localize6.0ms (0.2%)

series11.0ms (0.4%)

rewrite52.0ms (2.1%)

simplify135.0ms (5.4%)

prune59.0ms (2.3%)

localize5.0ms (0.2%)

series10.0ms (0.4%)

rewrite65.0ms (2.6%)

simplify151.0ms (6%)

prune26.0ms (1%)

localize10.0ms (0.4%)

series142.0ms (5.6%)

rewrite58.0ms (2.3%)

simplify84.0ms (3.3%)

prune120.0ms (4.8%)

regimes157.0ms (6.2%)

simplify2.0ms (0.1%)

end85.0ms (3.4%)

Profiling