Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.5s (44.7%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
463×	`fma-neg_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	185	17
3	915	13
4	2340	13
5	4455	13
6	4958	13
7	5077	13

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	46.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.5b	(/.f64 1 (*.f64 i i))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))
2.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))

rewrite78.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

77× egg-rr

Counts

3 → 77

Calls

2 calls:

77.0ms	((/.f64 1 (.f64 i i)) (/.f64 1/4 (-.f64 4 (/.f64 1 (.f64 i i)))) (-.f64 4 (/.f64 1 (*.f64 i i))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	202	21
2	2288	21
3	5374	21
0	0	0
1	0	0

simplify76.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

590×	`distribute-rgt-neg-in_binary64`
538×	`distribute-lft-neg-in_binary64`
472×	`associate-l_binary64`
438×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`

Counts

113 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	372
1	108	370
2	290	366
3	871	366
4	2646	366
5	4704	366
6	4924	366

prune65.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Error

0.0b

Counts

101 → 3

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	46.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	30.6b	(neg.f64 (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 1279 to 1067 computations (16.6% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
✓	0.0b	(fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
✓	0.0b	(*.f64 i (fma.f64 i i 1/4))

series13.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
5.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
3.0ms	(*.f64 i (fma.f64 i i 1/4))

rewrite70.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

103× egg-rr

Counts

3 → 103

Calls

2 calls:

67.0ms	((.f64 i (fma.f64 i i 1/4)) (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	294	47
2	2892	47
3	4969	47
0	0	0
1	0	0

simplify184.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

748×	`unswap-sqr_binary64`
714×	`distribute-rgt-out_binary64`
623×	`sqr-pow_binary64`
596×	`distribute-lft-out_binary64`
568×	`*-commutative_binary64`

Counts

139 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	452
1	64	432
2	153	420
3	411	420
4	1485	420
5	3328	420
6	3320	420
7	3674	420
8	4015	420
9	4425	420
10	4308	420
11	4708	420
12	4703	420
13	4935	420
14	4870	420

prune128.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	119	3	122

Error

0.0b

Counts

122 → 3

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
▶	46.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	30.6b	(neg.f64 (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 2940 to 2101 computations (28.5% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
✓	0.1b	(.f64 (.f64 i i) (*.f64 i i))
✓	15.0b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	42.4b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

series11.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
3.0ms	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))
2.0ms	(.f64 (.f64 i i) (*.f64 i i))
2.0ms	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)

rewrite89.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

159× egg-rr

Counts

4 → 159

Calls

2 calls:

86.0ms

((/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1)) (*.f64 (*.f64 i i) (*.f64 i i)) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	61
1	255	48
2	3542	48
3	4998	48
0	0	0
1	0	0

simplify101.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

602×	`distribute-rgt-neg-in_binary64`
550×	`distribute-lft-neg-in_binary64`
485×	`associate-l_binary64`
444×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`

Counts

207 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	408
1	110	406
2	292	402
3	864	402
4	2624	402
5	4683	402
6	4968	402
7	4932	402

prune125.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	181	3	184

Error

Counts

184 → 3

Alt Table

Status	Error	Program
✓	30.6b	(neg.f64 (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
▶	47.3b	(.f64 (/.f64 (pow.f64 i 4) (fma.f64 i 2 1)) (/.f64 (/.f64 1/4 (.f64 i i)) (fma.f64 i 2 -1)))

Compiler

Compiled 4294 to 2906 computations (32.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1/4 (*.f64 i i)) (fma.f64 i 2 -1))
✓	0.5b	(/.f64 1/4 (*.f64 i i))
✓	2.8b	(/.f64 (pow.f64 i 4) (fma.f64 i 2 1))
✓	43.7b	(.f64 (/.f64 (pow.f64 i 4) (fma.f64 i 2 1)) (/.f64 (/.f64 1/4 (.f64 i i)) (fma.f64 i 2 -1)))

series13.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(/.f64 (/.f64 1/4 (*.f64 i i)) (fma.f64 i 2 -1))
4.0ms	(.f64 (/.f64 (pow.f64 i 4) (fma.f64 i 2 1)) (/.f64 (/.f64 1/4 (.f64 i i)) (fma.f64 i 2 -1)))
3.0ms	(/.f64 (pow.f64 i 4) (fma.f64 i 2 1))
2.0ms	(/.f64 1/4 (*.f64 i i))

rewrite108.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

156× egg-rr

Counts

4 → 156

Calls

2 calls:

105.0ms

((*.f64 (/.f64 (pow.f64 i 4) (fma.f64 i 2 1)) (/.f64 (/.f64 1/4 (*.f64 i i)) (fma.f64 i 2 -1))) (/.f64 (pow.f64 i 4) (fma.f64 i 2 1)) (/.f64 1/4 (*.f64 i i)) (/.f64 (/.f64 1/4 (*.f64 i i)) (fma.f64 i 2 -1)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	321	59
2	3936	59
3	4844	59
0	0	0
1	0	0

simplify62.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

863×	`fma-neg_binary64`
673×	`cancel-sign-sub-inv_binary64`
391×	`unswap-sqr_binary64`
343×	`fma-def_binary64`
266×	`sub-neg_binary64`

Counts

204 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	699
1	258	675
2	715	659
3	2067	643
4	4122	643
5	4935	643

prune199.0ms (6.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	202	3	205

Error

Counts

205 → 3

Alt Table

Status	Error	Program
✓	30.6b	(neg.f64 (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	47.3b	(.f64 (/.f64 (pow.f64 i 4) (fma.f64 i 2 1)) (/.f64 (/.f64 1/4 (.f64 i i)) (fma.f64 i 2 -1)))

Compiler

Compiled 4500 to 3293 computations (26.8% saved)

regimes270.0ms (8.2%)

Accuracy

Total 0.3b remaining (99%)

Threshold costs 0.3b (99%)

Counts

113 → 1

Compiler

Compiled 4376 to 3271 computations (25.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	19	13
3	21	13
4	22	13
5	20	13

end103.0ms (3.1%)

Compiler: Compiled 70 to 53 computations (24.3% saved)

Details

analyze7.0ms (0.2%)

sample1.5s (44.7%)

simplify55.0ms (1.7%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite78.0ms (2.4%)

simplify76.0ms (2.3%)

prune65.0ms (2%)

localize12.0ms (0.3%)

series13.0ms (0.4%)

rewrite70.0ms (2.1%)

simplify184.0ms (5.6%)

prune128.0ms (3.9%)

localize20.0ms (0.6%)

series11.0ms (0.3%)

rewrite89.0ms (2.7%)

simplify101.0ms (3.1%)

prune125.0ms (3.8%)

localize11.0ms (0.3%)

series13.0ms (0.4%)

rewrite108.0ms (3.3%)

simplify62.0ms (1.9%)

prune199.0ms (6.1%)

regimes270.0ms (8.2%)

simplify2.0ms (0.1%)

end103.0ms (3.1%)

Profiling