Details

analyze96.0ms (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
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)

sample779.0ms (40.9%)

Results

763.0ms	8256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 36 to 16 computations (55.6% saved)

preprocess16.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

54×	`fma-def_binary64`
8×	`*-commutative_binary64`
8×	`associate-+l+_binary64`
8×	`associate-r_binary64`
6×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	25	30
2	52	22
3	91	22
4	125	22
5	137	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 17 to 7 computations (58.8% saved)

simplify12.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	51	11
4	69	11
5	75	11

Stop Event

1×

saturated

Counts

1 → 2

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

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(fma.f64 y (.f64 y 3) (.f64 x x))	x	inf
1.0ms	(fma.f64 y (.f64 y 3) (.f64 x x))	x	-inf
1.0ms	(fma.f64 y (.f64 y 3) (.f64 x x))	y	-inf
1.0ms	(fma.f64 y (.f64 y 3) (.f64 x x))	y	0
1.0ms	(fma.f64 y (.f64 y 3) (.f64 x x))	y	inf

rewrite35.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	140	11
2	1600	11

Stop Event

1×	node limit

Counts

1 → 29

simplify64.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
591×	`associate-l_binary64`
372×	`cube-prod_binary64`
330×	`associate-r_binary64`
284×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	231
1	20	231
2	36	231
3	67	231
4	152	231
5	441	231
6	1734	231
7	2049	231
8	2327	231
9	2578	231
10	2919	231
11	3416	231
12	4073	231
13	4861	231

Stop Event

1×	node limit

Counts

53 → 35

prune23.0ms (1.2%)

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
	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) 3)
▶	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 534 to 311 computations (41.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.2b	(.f64 3 (.f64 y y))

series10.0ms (0.5%)

Counts

2 → 36

Calls

9 calls:

2.0ms	(fma.f64 x x (.f64 3 (.f64 y y)))	x	-inf
1.0ms	(fma.f64 x x (.f64 3 (.f64 y y)))	x	inf
1.0ms	(fma.f64 x x (.f64 3 (.f64 y y)))	x	0
1.0ms	(fma.f64 x x (.f64 3 (.f64 y y)))	y	-inf
1.0ms	(fma.f64 x x (.f64 3 (.f64 y y)))	y	inf

rewrite57.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`log1p-expm1-u_binary64`
571×	`expm1-log1p-u_binary64`
309×	`log-prod_binary64`
130×	`prod-diff_binary64`
121×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	141	18
2	1608	18

Stop Event

1×	node limit

Counts

2 → 45

simplify69.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
607×	`associate-l_binary64`
372×	`cube-prod_binary64`
347×	`associate-r_binary64`
284×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	315
1	20	315
2	36	315
3	67	315
4	154	315
5	463	315
6	1791	315
7	2102	315
8	2380	315
9	2631	315
10	2972	315
11	3470	315
12	4125	315
13	4915	315

Stop Event

1×	node limit

Counts

81 → 51

prune31.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	50	5	55

Error

0.0b

Counts

55 → 5

Alt Table

Status	Error	Program
	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
▶	0.1b	(+.f64 0 (fma.f64 3 (.f64 y y) (.f64 x x)))
	14.8b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 736 to 384 computations (47.8% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.6%)

Counts

1 → 24

Calls

6 calls:

3.0ms	(fma.f64 3 (.f64 y y) (.f64 x x))	x	inf
2.0ms	(fma.f64 3 (.f64 y y) (.f64 x x))	x	-inf
2.0ms	(fma.f64 3 (.f64 y y) (.f64 x x))	x	0
1.0ms	(fma.f64 3 (.f64 y y) (.f64 x x))	y	-inf
1.0ms	(fma.f64 3 (.f64 y y) (.f64 x x))	y	inf

rewrite32.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

538×	`log1p-expm1-u_binary64`
538×	`expm1-log1p-u_binary64`
274×	`log-prod_binary64`
166×	`pow2_binary64`
115×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	139	11
2	1550	11

Stop Event

1×	node limit

Counts

1 → 30

simplify65.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
591×	`associate-l_binary64`
372×	`cube-prod_binary64`
330×	`associate-r_binary64`
284×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	231
1	20	231
2	36	231
3	67	231
4	152	231
5	441	231
6	1734	231
7	2049	231
8	2327	231
9	2578	231
10	2919	231
11	3416	231
12	4073	231
13	4861	231

Stop Event

1×	node limit

Counts

54 → 36

prune50.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	36	5	41

Error

0.0b

Counts

41 → 5

Alt Table

Status	Error	Program
▶	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
✓	0.1b	(+.f64 0 (fma.f64 3 (.f64 y y) (.f64 x x)))
	14.8b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 600 to 345 computations (42.5% saved)

localize25.0ms (1.3%)

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)
✓	20.2b	(sqrt.f64 (.f64 y (.f64 y 3)))

series106.0ms (5.5%)

Counts

4 → 72

Calls

18 calls:

18.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)	x	-inf
15.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)	x	inf
14.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)	y	-inf
13.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)	y	inf
12.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)	y	0

rewrite51.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	206	33
2	2230	33

Stop Event

1×	node limit

Counts

4 → 87

simplify34.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

714×	`times-frac_binary64`
328×	`associate-/l*_binary64`
300×	`associate-r_binary64`
291×	`associate-/r*_binary64`
262×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	1351
1	214	1062
2	791	1038

Stop Event

1×	node limit

Counts

159 → 123

prune92.0ms (4.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	123	5	128

Error

0.0b

Counts

128 → 5

Alt Table

Status	Error	Program
	27.1b	(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
✓	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
✓	0.1b	(+.f64 0 (fma.f64 3 (.f64 y y) (.f64 x x)))
	14.8b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 1967 to 1471 computations (25.2% saved)

regimes154.0ms (8.1%)

Accuracy

Total 0.1b remaining (90.5%)

Threshold costs 0.1b (90.5%)

Counts

28 → 1

Compiler

Compiled 1754 to 1235 computations (29.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11

Stop Event

1×

saturated

end65.0ms (3.4%)

Stop Event

1×

fuel

Compiler

Compiled 75 to 52 computations (30.7% saved)

Details

analyze96.0ms (5%)

sample779.0ms (40.9%)

preprocess16.0ms (0.8%)

simplify12.0ms (0.6%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series7.0ms (0.4%)

rewrite35.0ms (1.8%)

simplify64.0ms (3.4%)

prune23.0ms (1.2%)

localize5.0ms (0.2%)

series10.0ms (0.5%)

rewrite57.0ms (3%)

simplify69.0ms (3.6%)

prune31.0ms (1.6%)

localize5.0ms (0.3%)

series11.0ms (0.6%)

rewrite32.0ms (1.7%)

simplify65.0ms (3.4%)

prune50.0ms (2.6%)

localize25.0ms (1.3%)

series106.0ms (5.5%)

rewrite51.0ms (2.7%)

simplify34.0ms (1.8%)

prune92.0ms (4.8%)

regimes154.0ms (8.1%)

simplify2.0ms (0.1%)

end65.0ms (3.4%)

Profiling