Details

analyze8.0ms (0.2%)

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)

sample1.6s (37.8%)

Results

495.0ms	4496×	body	128	valid
478.0ms	1378×	body	1024	valid
451.0ms	1623×	body	512	valid
159.0ms	759×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify17.0ms (0.4%)

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)

localize12.0ms (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)))
3.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite350.0ms (8.2%)

Algorithm

4×	egg-rewrite

Rules

130×	`egg`
67×	`egg`
45×	`egg`
44×	`egg`

Counts

4 → 286

Calls

4 calls:

97.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
86.0ms	(/.f64 1 (-.f64 x 1))
82.0ms	(/.f64 1 (+.f64 x 1))
79.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	272	22
2	3856	22
3	4912	22
0	8	13
1	192	13
2	2534	13
3	4736	13
4	4934	13
0	5	7
1	109	7
2	1241	7
3	4766	7
4	5525	7
0	5	7
1	109	7
2	1254	7
3	4824	7
4	5558	7

simplify154.0ms (3.6%)

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

334 → 336

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

prune314.0ms (7.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	333	3	336
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	334	3	337

Error

0.3b

Counts

337 → 3

Alt Table

Status	Error	Program
	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))
	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))))))

Compiler

Compiled 8402 to 6704 computations (20.2% 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 (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(+.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))

rewrite305.0ms (7.1%)

Algorithm

3×	egg-rewrite

Rules

65×	`egg`
47×	`egg`
43×	`egg`

Counts

3 → 155

Calls

3 calls:

125.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x)))
89.0ms	(+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (+.f64 1 x))) (/.f64 -2 x))
88.0ms	(/.f64 1 (+.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	193	16
2	2608	16
3	5061	16
0	11	22
1	273	22
2	3917	22
3	4946	22
0	5	7
1	108	7
2	1267	7
3	4877	7
4	5689	7

simplify79.0ms (1.9%)

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

191 → 196

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

prune193.0ms (4.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	254	3	257

Error

0.3b

Counts

257 → 3

Alt Table

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

Compiler

Compiled 6023 to 4826 computations (19.9% saved)

localize11.0ms (0.3%)

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))

series14.0ms (0.3%)

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))

rewrite298.0ms (6.9%)

Algorithm

4×	egg-rewrite

Rules

80×	`egg`
64×	`egg`
62×	`egg`
58×	`egg`

Counts

4 → 264

Calls

4 calls:

82.0ms	(*.f64 (fma.f64 x x -1) x)
82.0ms	(/.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))
68.0ms	(+.f64 (.f64 (+.f64 (-.f64 x 1) (+.f64 1 x)) x) (.f64 (fma.f64 x x -1) -2))
60.0ms	(+.f64 (-.f64 x 1) (+.f64 1 x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	271	15
2	3491	15
3	5314	15
0	6	10
1	145	4
2	1995	4
3	5251	4
0	5	8
1	94	8
2	1028	8
3	4706	8
4	5898	8
0	14	31
1	319	25
2	4346	25
3	5082	25

simplify128.0ms (3%)

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

312 → 280

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

prune189.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	279	1	280
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	280	3	283

Error

0.3b

Counts

283 → 3

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 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))
	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))))))

Compiler

Compiled 8255 to 5113 computations (38.1% saved)

localize4.0ms (0.1%)

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))

rewrite46.0ms (1.1%)

Algorithm

1×	egg-rewrite

Rules

41× egg

Counts

1 → 41

Calls

1 calls:

45.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

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

simplify98.0ms (2.3%)

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

53 → 54

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

prune135.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	118	4	122

Error

0.0b

Counts

122 → 4

Alt Table

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

Compiler

Compiled 1617 to 1150 computations (28.9% saved)

regimes189.0ms (4.4%)

Accuracy

Total 0.0b remaining (73.5%)

Threshold costs 0.0b (73.5%)

Counts

58 → 1

Compiler

Compiled 1716 to 1324 computations (22.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	7	11

end85.0ms (2%)

Compiler: Compiled 58 to 41 computations (29.3% 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

analyze8.0ms (0.2%)

sample1.6s (37.8%)

simplify17.0ms (0.4%)

prune3.0ms (0.1%)

localize12.0ms (0.3%)

series11.0ms (0.3%)

rewrite350.0ms (8.2%)

simplify154.0ms (3.6%)

prune314.0ms (7.3%)

localize8.0ms (0.2%)

series9.0ms (0.2%)

rewrite305.0ms (7.1%)

simplify79.0ms (1.9%)

prune193.0ms (4.5%)

localize11.0ms (0.3%)

series14.0ms (0.3%)

rewrite298.0ms (6.9%)

simplify128.0ms (3%)

prune189.0ms (4.4%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite46.0ms (1.1%)

simplify98.0ms (2.3%)

prune135.0ms (3.1%)

regimes189.0ms (4.4%)

simplify2.0ms (0%)

end85.0ms (2%)

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