Details

analyze9.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.7s (50.9%)

Results

508.0ms	1378×	body	1024	valid
489.0ms	1623×	body	512	valid
478.0ms	4496×	body	128	valid
145.0ms	759×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify73.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

9.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	1.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series11.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite142.0ms (4.3%)

Algorithm

2×	batch-egg-rewrite

Rules

166× egg-rr

Counts

4 → 166

Calls

2 calls:

83.0ms	((+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))) (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 x 1)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	272	49
2	3856	49
3	4912	49
0	0	0
1	0	0

simplify82.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-neg_binary64`
489×	`cancel-sign-sub-inv_binary64`
328×	`sub-neg_binary64`
312×	`times-frac_binary64`
273×	`unsub-neg_binary64`

Counts

214 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	752
1	246	726
2	697	720
3	1844	717
4	4130	717
5	4617	717
6	4921	717

prune201.0ms (6.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	217	3	220

Error

0.3b

Counts

220 → 3

Alt Table

Status	Error	Program
	30.7b	(+.f64 (.f64 2 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 9))) (.f64 2 (/.f64 1 (pow.f64 x 3))))))
	29.2b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (-.f64 x 1) (*.f64 x (+.f64 1 x))))
▶	9.1b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))

Compiler

Compiled 5140 to 4072 computations (20.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 1 x))
	0.0b	(/.f64 1 (-.f64 x 1))
✓	1.9b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
✓	3.2b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x)))

series9.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))
3.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x)))
2.0ms	(/.f64 1 (+.f64 1 x))

rewrite85.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

133× egg-rr

Counts

3 → 133

Calls

2 calls:

79.0ms	((+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x)) (/.f64 1 (+.f64 1 x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	274	45
2	3882	45
3	4928	45
0	0	0
1	0	0

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

574×	`sub-neg_binary64`
367×	`fma-def_binary64`
314×	`associate-l_binary64`
291×	`times-frac_binary64`
264×	`distribute-lft-out_binary64`

Counts

169 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	595
1	222	581
2	670	569
3	1937	568
4	4176	568
5	5086	568

prune178.0ms (5.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	213	3	216

Error

0.3b

Counts

216 → 3

Alt Table

Status	Error	Program
	30.7b	(+.f64 (.f64 2 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 9))) (.f64 2 (/.f64 1 (pow.f64 x 3))))))
▶	29.2b	(/.f64 (-.f64 (.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (.f64 (fma.f64 x x -1) 2)) (*.f64 (fma.f64 x x -1) x))
✓	9.1b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))

Compiler

Compiled 4917 to 3935 computations (20% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (.f64 (fma.f64 x x -1) 2)) (*.f64 (fma.f64 x x -1) x))
✓	0.0b	(*.f64 (fma.f64 x x -1) x)
✓	3.2b	(+.f64 (-.f64 x 1) (+.f64 1 x))
✓	21.4b	(-.f64 (.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (.f64 (fma.f64 x x -1) 2))

series13.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(/.f64 (-.f64 (.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (.f64 (fma.f64 x x -1) 2)) (*.f64 (fma.f64 x x -1) x))
4.0ms	(-.f64 (.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (.f64 (fma.f64 x x -1) 2))
3.0ms	(*.f64 (fma.f64 x x -1) x)
2.0ms	(+.f64 (-.f64 x 1) (+.f64 1 x))

rewrite106.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

161× egg-rr

Counts

4 → 161

Calls

2 calls:

100.0ms

((-.f64 (*.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (*.f64 (fma.f64 x x -1) 2)) (+.f64 (-.f64 x 1) (+.f64 1 x)) (*.f64 (fma.f64 x x -1) x) (/.f64 (-.f64 (*.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (*.f64 (fma.f64 x x -1) 2)) (*.f64 (fma.f64 x x -1) x)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	74
1	330	52
2	4676	52
3	5053	52
0	0	0
1	0	0

simplify111.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

789×	`times-frac_binary64`
600×	`fma-def_binary64`
446×	`fma-neg_binary64`
306×	`sub-neg_binary64`
292×	`div-sub_binary64`

Counts

209 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	357
1	132	351
2	373	345
3	1020	345
4	2561	345
5	3552	345
6	4727	345
7	4840	345
8	4998	345
9	4884	345

prune126.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

0.3b

Counts

184 → 3

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 2 (*.f64 (fma.f64 x x -1) x))
	30.7b	(+.f64 (.f64 2 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 9))) (.f64 2 (/.f64 1 (pow.f64 x 3))))))
✓	9.1b	(-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 2 x))

Compiler

Compiled 5320 to 3269 computations (38.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (fma.f64 x x -1) x)
✓	0.3b	(/.f64 2 (*.f64 (fma.f64 x x -1) x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 2 (*.f64 (fma.f64 x x -1) x))

rewrite72.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

26× egg-rr

Counts

1 → 26

Calls

2 calls:

72.0ms	((/.f64 2 (*.f64 (fma.f64 x x -1) x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	144	11
2	1664	11
3	5067	11
0	0	0
1	0	0

simplify89.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

789×	`times-frac_binary64`
599×	`fma-def_binary64`
469×	`sub-neg_binary64`
448×	`fma-neg_binary64`
282×	`associate-/r*_binary64`

Counts

38 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	223
1	127	217
2	362	211
3	1001	211
4	2512	211
5	3419	211
6	4611	211
7	4834	211
8	5079	211

prune56.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	60	4	64

Error

0.0b

Counts

64 → 4

Alt Table

Status	Error	Program
	0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	21.4b	(pow.f64 (sqrt.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1)))) 2)
	0.1b	(*.f64 (/.f64 2 (fma.f64 x x -1)) (/.f64 1 x))
	0.3b	(.f64 (/.f64 1 (.f64 x (fma.f64 x x -1))) 2)

Compiler

Compiled 798 to 598 computations (25.1% saved)

regimes94.0ms (2.8%)

Accuracy

Total 0.1b remaining (77.4%)

Threshold costs 0.1b (77.4%)

Counts

50 → 1

Compiler

Compiled 1534 to 1198 computations (21.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	12	14
2	11	14

end60.0ms (1.8%)

Compiler: Compiled 64 to 47 computations (26.6% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze9.0ms (0.3%)

sample1.7s (50.9%)

simplify73.0ms (2.2%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series11.0ms (0.3%)

rewrite142.0ms (4.3%)

simplify82.0ms (2.5%)

prune201.0ms (6.1%)

localize8.0ms (0.2%)

series9.0ms (0.3%)

rewrite85.0ms (2.6%)

simplify61.0ms (1.8%)

prune178.0ms (5.4%)

localize14.0ms (0.4%)

series13.0ms (0.4%)

rewrite106.0ms (3.2%)

simplify111.0ms (3.4%)

prune126.0ms (3.8%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite72.0ms (2.2%)

simplify89.0ms (2.7%)

prune56.0ms (1.7%)

regimes94.0ms (2.8%)

simplify2.0ms (0.1%)

end60.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22