Details

analyze22.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	64×	body	512	valid
5.0ms	134×	body	128	valid
3.0ms	45×	body	256	valid
2.0ms	13×	body	1024	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
13×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

16.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.3b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 47 to 39 computations (17% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	2.8b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite169.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

870×	`*-un-lft-identity_binary64`
804×	`times-frac_binary64`
733×	`add-sqr-sqrt_binary64`
486×	`prod-diff_binary64`
465×	`add-cube-cbrt_binary64`

Counts

3 → 661

Calls

3 calls:

34.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify600.0ms (16.7%)

Algorithm

1×	egg-herbie

Rules

947×	`fma-neg_binary64`
335×	`times-frac_binary64`
236×	`distribute-rgt-in_binary64`
231×	`div-sub_binary64`
202×	`associate-/l*_binary64`

Counts

697 → 531

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	27782
1	632	18403
2	1772	13759
3	3945	12706
4	4972	12706
5	4989	12706
6	4909	12706

prune650.0ms (18.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	528	3	531
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	529	3	532

Error

0.4b

Counts

532 → 3

Alt Table

Status	Error	Program
	29.9b	(-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4)))
	16.3b	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -1 (+.f64 x -1)))
▶	15.7b	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))

Compiler

Compiled 23091 to 19170 computations (17% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
✓	2.2b	(-.f64 x (+.f64 2 x))

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
1.0ms	(-.f64 x (+.f64 2 x))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
12×	`prod-diff_binary64`

Counts

2 → 81

Calls

2 calls:

7.0ms	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
6.0ms	(-.f64 x (+.f64 2 x))

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-def_binary64`
468×	`associate-r_binary64`
325×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`
260×	`div-sub_binary64`

Counts

105 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1716
1	371	1547
2	1143	1129
3	4408	1129
4	4877	1129

prune78.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	126	4	130

Error

0.3b

Counts

130 → 4

Alt Table

Status	Error	Program
	29.8b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
	0.7b	(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
▶	0.4b	(/.f64 -2 (fma.f64 x x -1))

Compiler

Compiled 2457 to 1691 computations (31.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 -2 (fma.f64 x x -1))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 -2 (fma.f64 x x -1))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

3.0ms

(/.f64 -2 (fma.f64 x x -1))

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

741×	`fma-def_binary64`
662×	`fma-neg_binary64`
373×	`unswap-sqr_binary64`
363×	`associate-l_binary64`
341×	`associate-/r*_binary64`

Counts

41 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	680
1	194	628
2	483	625
3	1288	622
4	4089	622
5	5299	622

prune33.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Error

0.3b

Counts

52 → 4

Alt Table

Status	Error	Program
	29.8b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
▶	0.7b	(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
✓	0.4b	(/.f64 -2 (fma.f64 x x -1))

Compiler

Compiled 749 to 567 computations (24.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
✓	0.2b	(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
✓	15.9b	(cbrt.f64 (fma.f64 x x -1))

series30.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
8.0ms	(cbrt.f64 (fma.f64 x x -1))
7.0ms	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
5.0ms	(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

7.0ms	(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
4.0ms	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
4.0ms	(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
1.0ms	(cbrt.f64 (fma.f64 x x -1))

simplify172.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
504×	`times-frac_binary64`
334×	`fma-neg_binary64`
329×	`associate-/l/_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

200 → 295

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	5397
1	703	5006
2	2070	4484
3	4719	4484
4	4985	4484
5	4923	4484

prune330.0ms (9.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	356	1	357
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	357	4	361

Error

0.3b

Counts

361 → 4

Alt Table

Status	Error	Program
	29.8b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓	0.7b	(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
	0.7b	(/.f64 (/.f64 (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
✓	0.4b	(/.f64 -2 (fma.f64 x x -1))

Compiler

Compiled 9723 to 7253 computations (25.4% saved)

regimes512.0ms (14.2%)

Accuracy

Total 0.0b remaining (13.1%)

Threshold costs 0.0b (13.1%)

Counts

150 → 1

Compiler

Compiled 14586 to 12086 computations (17.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample734.0ms (20.4%)

Algorithm

1×

intervals

Results

200.0ms	1940×	body	512	valid
171.0ms	4594×	body	128	valid
73.0ms	1032×	body	256	valid
58.0ms	434×	body	1024	valid

Compiler

Compiled 82 to 60 computations (26.8% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Details

analyze22.0ms (0.6%)

sample26.0ms (0.7%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series9.0ms (0.2%)

rewrite169.0ms (4.7%)

simplify600.0ms (16.7%)

prune650.0ms (18.1%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite20.0ms (0.5%)

simplify73.0ms (2%)

prune78.0ms (2.2%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify58.0ms (1.6%)

prune33.0ms (0.9%)

localize7.0ms (0.2%)

series30.0ms (0.8%)

rewrite29.0ms (0.8%)

simplify172.0ms (4.8%)

prune330.0ms (9.2%)

regimes512.0ms (14.2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample734.0ms (20.4%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16