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)

sample1.5s (21.6%)

Results

1.2s	8256×	body	128	valid
11.0ms	100×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify34.0ms (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))))
	0.2b	(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))))
✓	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(/.f64 1 (*.f64 x 9))

series53.0ms (0.8%)

Counts

4 → 38

Calls

4 calls:

22.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
21.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
9.0ms	(*.f64 3 (sqrt.f64 x))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite42.0ms (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:

15.0ms	(-.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))

simplify162.0ms (2.3%)

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

prune279.0ms (4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	230	6	236
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	231	7	238

Error

0.0b

Counts

238 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 1/9 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 1 (fma.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))) (/.f64 1/9 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)))))
	0.4b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 (.f64 (sqrt.f64 3) (sqrt.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 3) (sqrt.f64 (sqrt.f64 x))))))
	0.2b	(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 (/.f64 y 3) (sqrt.f64 x)))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 6864 to 4961 computations (27.7% saved)

localize8.0ms (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 (/.f64 1 x) 9)
	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
	0.3b	(*.f64 3 (sqrt.f64 x))

series29.0ms (0.4%)

Counts

2 → 26

Calls

2 calls:

27.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
2.0ms	(/.f64 (/.f64 1 x) 9)

rewrite107.0ms (1.5%)

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:

35.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
5.0ms	(/.f64 (/.f64 1 x) 9)

simplify326.0ms (4.7%)

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

prune969.0ms (13.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	594	4	598
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	599	6	605

Error

Counts

605 → 6

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

Compiler

Compiled 23908 to 17809 computations (25.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series34.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

21.0ms	(.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x))))
13.0ms	(/.f64 1 (*.f64 3 (sqrt.f64 x)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`div-exp_binary64`

Counts

2 → 64

Calls

2 calls:

7.0ms	(.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x))))
4.0ms	(/.f64 1 (*.f64 3 (sqrt.f64 x)))

simplify131.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
467×	`sqr-pow_binary64`
460×	`fabs-mul_binary64`
445×	`associate-/r/_binary64`
368×	`fma-neg_binary64`

Counts

76 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	808
1	166	693
2	484	692
3	1662	692
4	2027	692
5	2266	692
6	2704	692
7	3328	692
8	3893	692
9	4678	692
10	4935	692

prune242.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	217	6	223

Error

Counts

223 → 6

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 (sqrt.f64 (/.f64 1 x)) (/.f64 (sqrt.f64 (/.f64 1 x)) 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 1 (fma.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))) (/.f64 1/9 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))))

Compiler

Compiled 4991 to 3737 computations (25.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series45.0ms (0.6%)

Counts

2 → 26

Calls

2 calls:

23.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
22.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

rewrite248.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1215×	`times-frac_binary64`
1068×	`*-un-lft-identity_binary64`
994×	`add-sqr-sqrt_binary64`
729×	`add-cube-cbrt_binary64`
595×	`prod-diff_binary64`

Counts

2 → 831

Calls

2 calls:

58.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
6.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

simplify1.1s (15.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

857 → 766

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	792	78957
1	2182	41391
2	4989	41391
3	4977	41391

prune1.1s (15.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	807	0	807
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	807	6	813

Error

Counts

813 → 6

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 (sqrt.f64 (/.f64 1 x)) (/.f64 (sqrt.f64 (/.f64 1 x)) 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x)))))
	0.3b	(-.f64 1 (fma.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))) (/.f64 1/9 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))))

Compiler

Compiled 40058 to 25462 computations (36.4% saved)

regimes407.0ms (5.8%)

Accuracy

Total 0.2b remaining (90%)

Threshold costs 0.2b (90%)

Counts

128 → 1

Compiler

Compiled 7157 to 5815 computations (18.8% saved)

simplify3.0ms (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	14	21
1	22	21
2	33	21
3	46	21
4	51	21
5	53	21
6	51	21

end98.0ms (1.4%)

Compiler: Compiled 144 to 113 computations (21.5% 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%)

sample1.5s (21.6%)

simplify34.0ms (0.5%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series53.0ms (0.8%)

rewrite42.0ms (0.6%)

simplify162.0ms (2.3%)

prune279.0ms (4%)

localize8.0ms (0.1%)

series29.0ms (0.4%)

rewrite107.0ms (1.5%)

simplify326.0ms (4.7%)

prune969.0ms (13.9%)

localize10.0ms (0.1%)

series34.0ms (0.5%)

rewrite13.0ms (0.2%)

simplify131.0ms (1.9%)

prune242.0ms (3.5%)

localize8.0ms (0.1%)

series45.0ms (0.6%)

rewrite248.0ms (3.6%)

simplify1.1s (15.5%)

prune1.1s (15.2%)

regimes407.0ms (5.8%)

simplify3.0ms (0%)

end98.0ms (1.4%)

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