Details

analyze56.0ms (0.9%)

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)

sample1.2s (19.6%)

Results

921.0ms	8256×	body	128	valid
12.0ms	117×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify35.0ms (0.6%)

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

prune3.0ms (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
	0.3b	(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)

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

series66.0ms (1.1%)

Counts

4 → 38

Calls

4 calls:

31.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
26.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
7.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite47.0ms (0.8%)

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))))
7.0ms	(/.f64 1 (*.f64 x 9))
4.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms	(*.f64 3 (sqrt.f64 x))

simplify170.0ms (2.8%)

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

prune297.0ms (4.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	229	7	236
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	231	7	238

Error

0.0b

Counts

238 → 7

Alt Table

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

Compiler

Compiled 6850 to 4955 computations (27.7% 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)))
	0.2b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))

series54.0ms (0.9%)

Counts

2 → 26

Calls

2 calls:

28.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
26.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

rewrite247.0ms (4.1%)

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:

56.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
11.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))

simplify1.1s (18%)

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 (18.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	806	1	807
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	808	6	814

Error

0.0b

Counts

814 → 6

Alt Table

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

Compiler

Compiled 40158 to 25549 computations (36.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series38.0ms (0.6%)

Counts

4 → 13

Calls

4 calls:

16.0ms	(fma.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))) (/.f64 1/9 x))
15.0ms	(*.f64 y (sqrt.f64 (/.f64 1 x)))
5.0ms	(sqrt.f64 (/.f64 1 x))
2.0ms	(/.f64 1/9 x)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
29×	`sqrt-prod_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 106

Calls

4 calls:

7.0ms	(*.f64 y (sqrt.f64 (/.f64 1 x)))
2.0ms	(sqrt.f64 (/.f64 1 x))
2.0ms	(/.f64 1/9 x)
0.0ms	(fma.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))) (/.f64 1/9 x))

simplify148.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
468×	`sqr-pow_binary64`
342×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
326×	`associate-/l*_binary64`

Counts

119 → 134

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	125	1382
1	193	1310
2	416	1310
3	811	1310
4	1617	1310
5	3591	1310
6	4125	1244
7	4619	1244
8	4706	1244
9	5259	1244

prune168.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	135	5	140

Error

Counts

140 → 5

Alt Table

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

Compiler

Compiled 2691 to 2045 computations (24% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1/9 x))
✓	0.2b	(fma.f64 y (sqrt.f64 (/.f64 1/9 x)) (/.f64 1/9 x))
	0.3b	(/.f64 1/9 x)

series24.0ms (0.4%)

Counts

2 → 13

Calls

2 calls:

18.0ms	(fma.f64 y (sqrt.f64 (/.f64 1/9 x)) (/.f64 1/9 x))
7.0ms	(sqrt.f64 (/.f64 1/9 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

3.0ms	(sqrt.f64 (/.f64 1/9 x))
0.0ms	(fma.f64 y (sqrt.f64 (/.f64 1/9 x)) (/.f64 1/9 x))

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

654×	`times-frac_binary64`
599×	`fma-def_binary64`
457×	`associate-/l*_binary64`
449×	`distribute-rgt-out_binary64`
394×	`distribute-rgt-in_binary64`

Counts

50 → 50

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	683
1	106	620
2	180	620
3	322	620
4	821	620
5	2781	620
6	4360	620
7	4319	620
8	4768	620
9	5086	620

prune156.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

Counts

125 → 5

Alt Table

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

Compiler

Compiled 2071 to 1524 computations (26.4% saved)

regimes898.0ms (15%)

Accuracy

Total 0.2b remaining (91.2%)

Threshold costs 0.2b (91.2%)

Counts

221 → 1

Compiler

Compiled 12389 to 9913 computations (20% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	16	19
2	20	19
3	22	19
4	23	19
5	22	19

end90.0ms (1.5%)

Compiler: Compiled 127 to 103 computations (18.9% 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

analyze56.0ms (0.9%)

sample1.2s (19.6%)

simplify35.0ms (0.6%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series66.0ms (1.1%)

rewrite47.0ms (0.8%)

simplify170.0ms (2.8%)

prune297.0ms (4.9%)

localize8.0ms (0.1%)

series54.0ms (0.9%)

rewrite247.0ms (4.1%)

simplify1.1s (18%)

prune1.1s (18.3%)

localize8.0ms (0.1%)

series38.0ms (0.6%)

rewrite16.0ms (0.3%)

simplify148.0ms (2.5%)

prune168.0ms (2.8%)

localize6.0ms (0.1%)

series24.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify97.0ms (1.6%)

prune156.0ms (2.6%)

regimes898.0ms (15%)

simplify3.0ms (0%)

end90.0ms (1.5%)

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