Details

analyze58.0ms (0.8%)

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)

sample262.0ms (3.7%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify35.0ms (0.5%)

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 (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

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

series61.0ms (0.9%)

Counts

4 → 38

Calls

4 calls:

26.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
25.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
8.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite40.0ms (0.6%)

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))))
5.0ms	(/.f64 1 (*.f64 x 9))
4.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms	(*.f64 3 (sqrt.f64 x))

simplify231.0ms (3.3%)

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

prune329.0ms (4.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	8	236
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

0.0b

Counts

238 → 9

Alt Table

Status	Error	Program
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) 3) (/.f64 (cbrt.f64 y) (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 1 (/.f64 (.f64 3 (sqrt.f64 x)) y)))
	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))))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	22.2b	(-.f64 (-.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (.f64 x 9) (.f64 x 9)) (.f64 x 9))))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (*.f64 3 (sqrt.f64 x)) (cbrt.f64 y))))
	25.5b	(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 1 3) (pow.f64 (/.f64 1 (.f64 x 9)) 3)) (.f64 3 (sqrt.f64 x))) (.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 1 (.f64 x 9)) (/.f64 1 (.f64 x 9))) (.f64 1 (/.f64 1 (.f64 x 9))))) y)) (.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 1 (.f64 x 9)) (/.f64 1 (.f64 x 9))) (.f64 1 (/.f64 1 (.f64 x 9))))) (.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 7074 to 5129 computations (27.5% saved)

localize10.0ms (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))))
	0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(/.f64 (/.f64 1 x) 9)
	0.3b	(*.f64 3 (sqrt.f64 x))

series26.0ms (0.4%)

Counts

2 → 26

Calls

2 calls:

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

rewrite102.0ms (1.4%)

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:

32.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
5.0ms	(/.f64 (/.f64 1 x) 9)

simplify309.0ms (4.4%)

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

prune1.1s (15.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	595	3	598
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	597	10	607

Error

0.0b

Counts

607 → 10

Alt Table

Status	Error	Program
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) 3) (/.f64 (cbrt.f64 y) (sqrt.f64 x))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 1 (/.f64 (.f64 3 (sqrt.f64 x)) y)))
	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))))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (*.f64 3 (sqrt.f64 x)) (cbrt.f64 y))))
	0.7b	(-.f64 (-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 1/9 (cbrt.f64 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.4b	(-.f64 (-.f64 1 (.f64 1/3 (/.f64 1/3 x))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	0.4b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 (neg.f64 (/.f64 1/9 (sqrt.f64 x))) (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 24054 to 17914 computations (25.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 3 (sqrt.f64 x)) y)
	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
	0.5b	(/.f64 1 (*.f64 x 9))

series39.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

25.0ms	(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
14.0ms	(/.f64 (*.f64 3 (sqrt.f64 x)) y)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
4.0ms	(/.f64 (*.f64 3 (sqrt.f64 x)) y)

simplify141.0ms (2%)

Algorithm

1×	egg-herbie

Rules

744×	`div-sub_binary64`
432×	`*-commutative_binary64`
368×	`associate-/l*_binary64`
281×	`sub-neg_binary64`
275×	`associate-/r*_binary64`

Counts

105 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1477
1	198	1284
2	622	1265
3	2287	1265
4	2702	1265
5	3041	1265
6	3954	1265
7	4231	1265
8	4936	1265
9	4833	1265

prune260.0ms (3.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	187	9	196

Error

0.0b

Counts

196 → 9

Alt Table

Status	Error	Program
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.3b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1/3 (/.f64 (sqrt.f64 x) y)))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (*.f64 3 (sqrt.f64 x)) (cbrt.f64 y))))
	0.7b	(-.f64 (-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 1/9 (cbrt.f64 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.4b	(-.f64 (-.f64 1 (.f64 1/3 (/.f64 1/3 x))) (/.f64 y (.f64 3 (sqrt.f64 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))))))
	0.4b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 (neg.f64 (/.f64 1/9 (sqrt.f64 x))) (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 4250 to 3100 computations (27.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1/3 (/.f64 (sqrt.f64 x) y)))
✓	0.2b	(/.f64 (sqrt.f64 x) y)
	0.5b	(/.f64 1 (*.f64 x 9))
✓	0.5b	(/.f64 1/3 (/.f64 (sqrt.f64 x) y))

series62.0ms (0.9%)

Counts

3 → 38

Calls

3 calls:

26.0ms	(/.f64 1/3 (/.f64 (sqrt.f64 x) y))
26.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1/3 (/.f64 (sqrt.f64 x) y)))
10.0ms	(/.f64 (sqrt.f64 x) y)

rewrite215.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

1133×	`times-frac_binary64`
971×	`*-un-lft-identity_binary64`
905×	`add-sqr-sqrt_binary64`
676×	`add-cube-cbrt_binary64`
518×	`prod-diff_binary64`

Counts

3 → 777

Calls

3 calls:

43.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1/3 (/.f64 (sqrt.f64 x) y)))
8.0ms	(/.f64 1/3 (/.f64 (sqrt.f64 x) y))
3.0ms	(/.f64 (sqrt.f64 x) y)

simplify920.0ms (13%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
440×	`associate-*l/_binary64`
347×	`associate-/r/_binary64`
249×	`fma-udef_binary64`
230×	`associate-/l*_binary64`

Counts

815 → 698

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	783	71892
1	2100	33166
2	4486	33124
3	5034	33124

prune1.3s (19.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	738	1	739
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	739	9	748

Error

0.0b

Counts

748 → 9

Alt Table

Status	Error	Program
	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 1 (/.f64 (sqrt.f64 x) (.f64 1/3 y))))
	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))))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
✓	0.3b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 1/3 (/.f64 (sqrt.f64 x) y)))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.7b	(-.f64 (-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 1/9 (cbrt.f64 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.4b	(-.f64 (-.f64 1 (.f64 1/3 (/.f64 1/3 x))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.4b	(+.f64 1 (fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (/.f64 (neg.f64 (/.f64 1/9 (sqrt.f64 x))) (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 3) (sqrt.f64 x)))))

Compiler

Compiled 35016 to 20564 computations (41.3% saved)

regimes577.0ms (8.2%)

Accuracy

Total 0.2b remaining (88.4%)

Threshold costs 0.2b (88.4%)

Counts

157 → 1

Compiler

Compiled 9614 to 7825 computations (18.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_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	28	21
3	40	21
4	47	21
5	51	21
6	52	21
7	50	21

end1.0ms (0%)

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

sample923.0ms (13.1%)

Algorithm

1×

intervals

Results

508.0ms	8000×	body	128	valid
6.0ms	107×	body	128	invalid

Compiler

Compiled 198 to 156 computations (21.2% 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

analyze58.0ms (0.8%)

sample262.0ms (3.7%)

simplify35.0ms (0.5%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series61.0ms (0.9%)

rewrite40.0ms (0.6%)

simplify231.0ms (3.3%)

prune329.0ms (4.7%)

localize10.0ms (0.1%)

series26.0ms (0.4%)

rewrite102.0ms (1.4%)

simplify309.0ms (4.4%)

prune1.1s (15.1%)

localize10.0ms (0.1%)

series39.0ms (0.6%)

rewrite15.0ms (0.2%)

simplify141.0ms (2%)

prune260.0ms (3.7%)

localize10.0ms (0.1%)

series62.0ms (0.9%)

rewrite215.0ms (3%)

simplify920.0ms (13%)

prune1.3s (19.1%)

regimes577.0ms (8.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample923.0ms (13.1%)

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