Details

analyze55.0ms (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)

sample1.2s (18%)

Results

920.0ms	8256×	body	128	valid
9.0ms	90×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% 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

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

series47.0ms (0.7%)

Counts

4 → 38

Calls

4 calls:

20.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
20.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
5.0ms	(*.f64 3 (sqrt.f64 x))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite38.0ms (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:

12.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
5.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify154.0ms (2.4%)

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

prune309.0ms (4.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	227	9	236
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	228	10	238

Error

Counts

238 → 10

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 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.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)))))
	0.4b	(-.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)))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	0.4b	(-.f64 (-.f64 1 (.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (/.f64 y (.f64 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 y (*.f64 3 (sqrt.f64 x))))
	17.9b	(-.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 1/9 x) 3))) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 6972 to 5051 computations (27.6% saved)

localize8.0ms (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))

series49.0ms (0.8%)

Counts

3 → 38

Calls

3 calls:

25.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
23.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
1.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))

rewrite231.0ms (3.5%)

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:

45.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
5.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
5.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))

simplify897.0ms (13.7%)

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

prune1.3s (19.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	864	0	864
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	864	10	874

Error

Counts

874 → 10

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 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.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)))))
	0.4b	(-.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)))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	0.4b	(-.f64 (-.f64 1 (.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (/.f64 y (.f64 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 y (*.f64 3 (sqrt.f64 x))))
	17.9b	(-.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 1/9 x) 3))) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 41973 to 27021 computations (35.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.2b	(*.f64 y (sqrt.f64 (/.f64 1 x)))
	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))

series28.0ms (0.4%)

Counts

3 → 0

Calls

3 calls:

14.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))
11.0ms	(*.f64 y (sqrt.f64 (/.f64 1 x)))
4.0ms	(sqrt.f64 (/.f64 1 x))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 88

Calls

3 calls:

6.0ms	(.f64 1/3 (.f64 y (sqrt.f64 (/.f64 1 x))))
5.0ms	(*.f64 y (sqrt.f64 (/.f64 1 x)))
2.0ms	(sqrt.f64 (/.f64 1 x))

simplify106.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

460×	`associate-/l*_binary64`
395×	`associate-l_binary64`
354×	`*-commutative_binary64`
326×	`associate-*l/_binary64`
301×	`associate-/r*_binary64`

Counts

88 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1020
1	154	963
2	403	962
3	939	962
4	1338	962
5	2435	962
6	3031	962
7	3633	962
8	4923	962
9	4922	962

prune189.0ms (2.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	140	10	150

Error

Counts

150 → 10

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 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.3b	(-.f64 (-.f64 1 (.f64 (/.f64 1 x) 1/9)) (/.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)))))
	0.4b	(-.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)))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	0.4b	(-.f64 (-.f64 1 (.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) (/.f64 y (.f64 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 y (*.f64 3 (sqrt.f64 x))))
	17.9b	(-.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 1/9 x) 3))) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 3317 to 2661 computations (19.8% 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)))
✓	0.3b	(/.f64 (/.f64 1 x) 9)
	0.3b	(*.f64 3 (sqrt.f64 x))

series22.0ms (0.3%)

Counts

2 → 26

Calls

2 calls:

20.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
1.0ms	(/.f64 (/.f64 1 x) 9)

rewrite98.0ms (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:

31.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
4.0ms	(/.f64 (/.f64 1 x) 9)

simplify301.0ms (4.6%)

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

prune959.0ms (14.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	597	1	598
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	598	10	608

Error

Counts

608 → 10

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 1 (.f64 x 9))) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
	0.4b	(-.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)))
	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 y (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x)))))
	0.4b	(-.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 (-.f64 1 (/.f64 (/.f64 1/3 x) (sqrt.f64 9))) (/.f64 y (*.f64 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 y (*.f64 3 (sqrt.f64 x))))
	17.9b	(-.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 1/9 x) 3))) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 23872 to 17788 computations (25.5% saved)

regimes350.0ms (5.4%)

Accuracy

Total 0.2b remaining (90.6%)

Threshold costs 0.2b (90.6%)

Counts

116 → 1

Compiler

Compiled 6314 to 5050 computations (20% saved)

simplify5.0ms (0.1%)

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

end149.0ms (2.3%)

Compiler: Compiled 220 to 179 computations (18.6% 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

analyze55.0ms (0.8%)

sample1.2s (18%)

simplify35.0ms (0.5%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series47.0ms (0.7%)

rewrite38.0ms (0.6%)

simplify154.0ms (2.4%)

prune309.0ms (4.7%)

localize8.0ms (0.1%)

series49.0ms (0.8%)

rewrite231.0ms (3.5%)

simplify897.0ms (13.7%)

prune1.3s (19.6%)

localize10.0ms (0.2%)

series28.0ms (0.4%)

rewrite18.0ms (0.3%)

simplify106.0ms (1.6%)

prune189.0ms (2.9%)

localize9.0ms (0.1%)

series22.0ms (0.3%)

rewrite98.0ms (1.5%)

simplify301.0ms (4.6%)

prune959.0ms (14.7%)

regimes350.0ms (5.4%)

simplify5.0ms (0.1%)

end149.0ms (2.3%)

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