Details

analyze625.0ms (6.7%)

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
0%	50%	50%	4
0%	50%	50%	5
6.2%	43.7%	50%	6
6.2%	43.7%	50%	7
9.4%	40.6%	50%	8
10.1%	39.4%	50.4%	9
12.1%	37.3%	50.6%	10
12.7%	36.4%	50.9%	11
13.4%	35.6%	51.1%	12
13.7%	35%	51.2%	13
13.7%	35%	51.3%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.5s (15.9%)

Results

1.0s	8256×	body	128	valid
199.0ms	260×	body	8192	exit
7.0ms	58×	body	128	invalid

Compiler

Compiled 33 to 27 computations (18.2% saved)

simplify37.0ms (0.4%)

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 3 (sqrt.f64 x))
✓	0.3b	(/.f64 1 (*.f64 x 9))

series59.0ms (0.6%)

Counts

4 → 38

Calls

4 calls:

25.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
24.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
8.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite39.0ms (0.4%)

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:

13.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
4.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify162.0ms (1.7%)

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

prune319.0ms (3.4%)

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

Counts

238 → 8

Alt Table

Status	Error	Program
▶	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 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 -1/9 x)))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (*.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))))
	0.5b	(-.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x 9))) (cbrt.f64 (/.f64 1 (.f64 x 9)))) (cbrt.f64 (/.f64 1 (.f64 x 9))))) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 6914 to 5003 computations (27.6% saved)

localize9.0ms (0.1%)

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))

series57.0ms (0.6%)

Counts

3 → 38

Calls

3 calls:

30.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
25.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
2.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))

rewrite249.0ms (2.7%)

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:

47.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
6.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
5.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))

simplify905.0ms (9.6%)

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

prune1.7s (17.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	862	2	864
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	865	7	872

Error

Counts

872 → 7

Alt Table

Status	Error	Program
	0.3b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 -1/9 x)))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	0.5b	(-.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 1/9 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 1/9 x)))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (*.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 41887 to 26948 computations (35.7% 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) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.2b	(/.f64 (/.f64 1 x) 9)
	0.3b	(*.f64 3 (sqrt.f64 x))

series56.0ms (0.6%)

Counts

2 → 26

Calls

2 calls:

54.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
2.0ms	(/.f64 (/.f64 1 x) 9)

rewrite104.0ms (1.1%)

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:

33.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
4.0ms	(/.f64 (/.f64 1 x) 9)

simplify311.0ms (3.3%)

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

prune934.0ms (9.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	597	1	598
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	598	7	605

Error

Counts

605 → 7

Alt Table

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

Compiler

Compiled 23930 to 17828 computations (25.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 y (sqrt.f64 x))
✓	0.2b	(/.f64 3 (/.f64 y (sqrt.f64 x)))
	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.8b	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))

series64.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

27.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
23.0ms	(/.f64 y (sqrt.f64 x))
14.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))

rewrite113.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

849×	`times-frac_binary64`
413×	`*-un-lft-identity_binary64`
413×	`add-sqr-sqrt_binary64`
413×	`add-cube-cbrt_binary64`
156×	`sqrt-prod_binary64`

Counts

3 → 463

Calls

3 calls:

14.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
7.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))
3.0ms	(/.f64 y (sqrt.f64 x))

simplify690.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-neg_binary64`
473×	`*-commutative_binary64`
345×	`fabs-mul_binary64`
344×	`associate-/r/_binary64`
295×	`fma-def_binary64`

Counts

499 → 583

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	320	11024
1	615	10136
2	1864	10009
3	2267	10009
4	2669	10009
5	2970	10009
6	3817	10009
7	4639	10009
8	4502	10009
9	4808	10009
10	4931	10009
11	4840	10009

prune717.0ms (7.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	624	0	624
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	624	7	631

Error

Counts

631 → 7

Alt Table

Status	Error	Program
	0.3b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 -1/9 x)))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1/9 (sqrt.f64 x)))) (/.f64 y (.f64 3 (sqrt.f64 x))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (*.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 17184 to 10780 computations (37.3% saved)

regimes617.0ms (6.6%)

Accuracy

Total 0.2b remaining (89.7%)

Threshold costs 0.2b (89.7%)

Counts

190 → 1

Compiler

Compiled 10796 to 8815 computations (18.3% 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	15	21
1	22	21
2	33	21
3	41	21
4	47	21
5	50	21
6	51	21
7	48	21

end120.0ms (1.3%)

Compiler: Compiled 163 to 129 computations (20.9% 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

analyze625.0ms (6.7%)

sample1.5s (15.9%)

simplify37.0ms (0.4%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series59.0ms (0.6%)

rewrite39.0ms (0.4%)

simplify162.0ms (1.7%)

prune319.0ms (3.4%)

localize9.0ms (0.1%)

series57.0ms (0.6%)

rewrite249.0ms (2.7%)

simplify905.0ms (9.6%)

prune1.7s (17.9%)

localize9.0ms (0.1%)

series56.0ms (0.6%)

rewrite104.0ms (1.1%)

simplify311.0ms (3.3%)

prune934.0ms (9.9%)

localize10.0ms (0.1%)

series64.0ms (0.7%)

rewrite113.0ms (1.2%)

simplify690.0ms (7.3%)

prune717.0ms (7.6%)

regimes617.0ms (6.6%)

simplify4.0ms (0%)

end120.0ms (1.3%)

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