Details

analyze58.0ms (1.6%)

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 (32.6%)

Results

930.0ms	8256×	body	128	valid
9.0ms	87×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify34.0ms (0.9%)

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

0.2b

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 (0.2%)

Local error

Found 4 expressions with local error:

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

series35.0ms (1%)

Counts

4 → 36

Calls

4 calls:

24.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
6.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(/.f64 1 (*.f64 x 9))
2.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`
21×	`prod-diff_binary64`

Counts

4 → 125

Calls

4 calls:

8.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
4.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
3.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-/l*_binary64`
514×	`fma-def_binary64`
439×	`associate-*l/_binary64`
356×	`associate-/r*_binary64`
323×	`associate-/l/_binary64`

Counts

161 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	1803
1	328	1417
2	1016	1288
3	4591	1288
4	4873	1288

prune199.0ms (5.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	151	7	158
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	152	8	160

Error

0.0b

Counts

160 → 8

Alt Table

Status	Error	Program
	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 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	11.9b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3))))
	0.3b	(-.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 1 9) (/.f64 1 x)))) (fma.f64 (neg.f64 (/.f64 1 9)) (/.f64 1 x) (.f64 (/.f64 1 9) (/.f64 1 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 1 (/.f64 -1/9 x))) (cbrt.f64 (+.f64 1 (/.f64 -1/9 x)))) (cbrt.f64 (+.f64 1 (/.f64 -1/9 x)))) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 3800 to 2918 computations (23.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(/.f64 (/.f64 1 x) 9)
1.0ms	(-.f64 1 (/.f64 (/.f64 1 x) 9))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

349×	`times-frac_binary64`
248×	`add-sqr-sqrt_binary64`
236×	`*-un-lft-identity_binary64`
228×	`add-cube-cbrt_binary64`
129×	`prod-diff_binary64`

Counts

2 → 271

Calls

2 calls:

16.0ms	(-.f64 1 (/.f64 (/.f64 1 x) 9))
4.0ms	(/.f64 (/.f64 1 x) 9)

simplify168.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-/l*_binary64`
528×	`times-frac_binary64`
393×	`fma-def_binary64`
379×	`associate-/l/_binary64`
204×	`distribute-neg-frac_binary64`

Counts

295 → 317

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	7339
1	629	4850
2	1649	3779
3	4820	3779
4	4690	3779

prune553.0ms (15.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	372	1	373
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	373	8	381

Error

0.0b

Counts

381 → 8

Alt Table

Status	Error	Program
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.4b	(-.f64 (-.f64 1 (.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (sqrt.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 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	11.9b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3))))
	0.3b	(-.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 1 9) (/.f64 1 x)))) (fma.f64 (neg.f64 (/.f64 1 9)) (/.f64 1 x) (.f64 (/.f64 1 9) (/.f64 1 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)))

Compiler

Compiled 13657 to 10592 computations (22.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 3 (sqrt.f64 x)) y)
	0.3b	(/.f64 1 (*.f64 x 9))
	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.6b	(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))

series36.0ms (1%)

Counts

2 → 24

Calls

2 calls:

24.0ms	(/.f64 1 (/.f64 (*.f64 3 (sqrt.f64 x)) y))
12.0ms	(/.f64 (*.f64 3 (sqrt.f64 x)) y)

rewrite12.0ms (0.3%)

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:

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

simplify143.0ms (3.9%)

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

prune253.0ms (6.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	186	8	194

Error

0.0b

Counts

194 → 8

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1 (*.f64 3 (sqrt.f64 x)))))
	0.4b	(-.f64 (-.f64 1 (.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (sqrt.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 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x)))))
✓	0.2b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	11.9b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3))))
	0.3b	(-.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 1 9) (/.f64 1 x)))) (fma.f64 (neg.f64 (/.f64 1 9)) (/.f64 1 x) (.f64 (/.f64 1 9) (/.f64 1 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)))

Compiler

Compiled 4216 to 3095 computations (26.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series43.0ms (1.2%)

Counts

2 → 12

Calls

2 calls:

26.0ms	(.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x))))
17.0ms	(/.f64 1 (*.f64 3 (sqrt.f64 x)))

rewrite16.0ms (0.4%)

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:

9.0ms	(.f64 y (/.f64 1 (.f64 3 (sqrt.f64 x))))
4.0ms	(/.f64 1 (*.f64 3 (sqrt.f64 x)))

simplify114.0ms (3.1%)

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

prune193.0ms (5.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	157	8	165

Error

0.0b

Counts

165 → 8

Alt Table

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

Compiler

Compiled 3345 to 2522 computations (24.6% saved)

regimes282.0ms (7.7%)

Accuracy

Total 0.2b remaining (85.8%)

Threshold costs 0.2b (85.8%)

Counts

88 → 1

Compiler

Compiled 6488 to 5335 computations (17.8% saved)

simplify6.0ms (0.2%)

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	41	21
4	47	21
5	49	21
6	47	21

end125.0ms (3.4%)

Compiler: Compiled 191 to 158 computations (17.3% 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 (1.6%)

sample1.2s (32.6%)

simplify34.0ms (0.9%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series35.0ms (1%)

rewrite23.0ms (0.6%)

simplify74.0ms (2%)

prune199.0ms (5.5%)

localize11.0ms (0.3%)

series3.0ms (0.1%)

rewrite51.0ms (1.4%)

simplify168.0ms (4.6%)

prune553.0ms (15.1%)

localize9.0ms (0.2%)

series36.0ms (1%)

rewrite12.0ms (0.3%)

simplify143.0ms (3.9%)

prune253.0ms (6.9%)

localize9.0ms (0.3%)

series43.0ms (1.2%)

rewrite16.0ms (0.4%)

simplify114.0ms (3.1%)

prune193.0ms (5.3%)

regimes282.0ms (7.7%)

simplify6.0ms (0.2%)

end125.0ms (3.4%)

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