Details

analyze295.0ms (2.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample24.0ms (0.2%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
309×	`fma-def_binary64`
228×	`cancel-sign-sub-inv_binary64`
83×	`associate-/l*_binary64`
72×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

prune4.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
✓	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(*.f64 3 (sqrt.f64 x))

series67.0ms (0.6%)

Counts

4 → 38

Calls

4 calls:

28.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
28.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64`
80×	`add-sqr-sqrt_binary64`
70×	`prod-diff_binary64`
50×	`add-cube-cbrt_binary64`
42×	`times-frac_binary64`

Counts

4 → 190

Calls

4 calls:

14.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
4.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
4.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify204.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
276×	`fma-neg_binary64`
266×	`exp-prod_binary64`
243×	`cancel-sign-sub-inv_binary64`
236×	`distribute-rgt-in_binary64`

Counts

228 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5841
1	609	3520
2	1862	2992
3	4354	2992
4	4859	2992
5	4769	2992

prune562.0ms (5.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	228	8	236
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	8	238

Error

0.0b

Counts

238 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	32.3b	(exp.f64 (log1p.f64 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 -1/9 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x))))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))

Compiler

Compiled 6870 to 4967 computations (27.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 1 (*.f64 x 9)))
✓	0.0b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))

series115.0ms (1.1%)

Counts

3 → 38

Calls

3 calls:

57.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
54.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
3.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))

rewrite467.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

1227×	`times-frac_binary64`
1089×	`*-un-lft-identity_binary64`
1014×	`add-sqr-sqrt_binary64`
746×	`add-cube-cbrt_binary64`
616×	`prod-diff_binary64`

Counts

3 → 879

Calls

3 calls:

106.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
13.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
12.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))

simplify1.5s (13.5%)

Algorithm

1×	egg-herbie

Rules

543×	`associate-*l/_binary64`
292×	`distribute-neg-frac_binary64`
264×	`associate-/l*_binary64`
263×	`fma-udef_binary64`
212×	`associate-/l/_binary64`

Counts

917 → 823

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	804	79307
1	2182	41990
2	4972	41990

prune2.0s (19%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	863	1	864
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	864	8	872

Error

0.0b

Counts

872 → 8

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	28.7b	(-.f64 (exp.f64 (log1p.f64 (/.f64 -1/9 x))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x))))))

Compiler

Compiled 41873 to 26939 computations (35.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(/.f64 (/.f64 1 x) 9)
	0.3b	(*.f64 3 (sqrt.f64 x))

series50.0ms (0.5%)

Counts

2 → 26

Calls

2 calls:

47.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
3.0ms	(/.f64 (/.f64 1 x) 9)

rewrite189.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

458×	`times-frac_binary64`
423×	`add-sqr-sqrt_binary64`
330×	`*-un-lft-identity_binary64`
261×	`add-cube-cbrt_binary64`
213×	`prod-diff_binary64`

Counts

2 → 370

Calls

2 calls:

55.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
8.0ms	(/.f64 (/.f64 1 x) 9)

simplify551.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-neg_binary64`
780×	`times-frac_binary64`
216×	`associate-*r/_binary64`
196×	`associate-*l/_binary64`
179×	`*-commutative_binary64`

Counts

396 → 542

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	378	14432
1	976	9574
2	2673	8625
3	4403	8501
4	4877	8501

prune2.5s (23.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	597	1	598
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	597	9	606

Error

Counts

606 → 9

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	28.7b	(-.f64 (exp.f64 (log1p.f64 (/.f64 -1/9 x))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 9 (sqrt.f64 x)))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x))))))

Compiler

Compiled 23966 to 17859 computations (25.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(*.f64 (/.f64 1 x) 1/9)

series43.0ms (0.4%)

Counts

2 → 26

Calls

2 calls:

30.0ms	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
14.0ms	(*.f64 (/.f64 1 x) 1/9)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
24×	`prod-diff_binary64`
23×	`times-frac_binary64`

Counts

2 → 92

Calls

2 calls:

7.0ms	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
5.0ms	(*.f64 (/.f64 1 x) 1/9)

simplify164.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-def_binary64`
341×	`associate-*l/_binary64`
248×	`fma-neg_binary64`
245×	`associate-*r/_binary64`
225×	`associate-/l*_binary64`

Counts

118 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2666
1	473	1760
2	1332	1505
3	4274	1497
4	4903	1497
5	4797	1497

prune413.0ms (3.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	201	9	210

Error

Counts

210 → 9

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
✓	0.2b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.f64 y (.f64 3 (sqrt.f64 x))))
	28.7b	(-.f64 (exp.f64 (log1p.f64 (/.f64 -1/9 x))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 9 (sqrt.f64 x)))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x))))))

Compiler

Compiled 4989 to 3512 computations (29.6% saved)

regimes400.0ms (3.7%)

Accuracy

Total 0.2b remaining (88.3%)

Threshold costs 0.2b (88.3%)

Counts

75 → 1

Compiler

Compiled 3959 to 3202 computations (19.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	20	21
2	31	21
3	39	21
4	45	21
5	48	21
6	49	21
7	47	21

end1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

sample1.0s (9.4%)

Algorithm

1×

intervals

Results

531.0ms	8000×	body	128	valid
6.0ms	93×	body	128	invalid

Compiler

Compiled 192 to 154 computations (19.8% saved)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Details

analyze295.0ms (2.7%)

sample24.0ms (0.2%)

simplify36.0ms (0.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series67.0ms (0.6%)

rewrite50.0ms (0.5%)

simplify204.0ms (1.9%)

prune562.0ms (5.2%)

localize18.0ms (0.2%)

series115.0ms (1.1%)

rewrite467.0ms (4.3%)

simplify1.5s (13.5%)

prune2.0s (19%)

localize16.0ms (0.2%)

series50.0ms (0.5%)

rewrite189.0ms (1.8%)

simplify551.0ms (5.1%)

prune2.5s (23.6%)

localize9.0ms (0.1%)

series43.0ms (0.4%)

rewrite18.0ms (0.2%)

simplify164.0ms (1.5%)

prune413.0ms (3.8%)

regimes400.0ms (3.7%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.0s (9.4%)

Profiling

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16