Details

analyze5.0ms (0.1%)

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)

sample84.0ms (2.5%)

Algorithm

1×

intervals

Results

44.0ms	14×	body	1024	valid
6.0ms	162×	body	128	valid
5.0ms	50×	body	512	valid
2.0ms	30×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify12.0ms (0.4%)

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

prune2.0ms (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

12.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.6b	(-.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))
✓	3.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series10.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
3.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(/.f64 1 (+.f64 x 1))

rewrite156.0ms (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:

38.0ms	(-.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))

simplify623.0ms (18.9%)

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

prune603.0ms (18.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	529	2	531
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	529	3	532

Error

0.5b

Counts

532 → 3

Alt Table

Status	Error	Program
✓	12.6b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
▶	11.5b	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
	35.6b	(+.f64 (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4))) (/.f64 -2 (pow.f64 x 6)))

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))
✓	1.9b	(-.f64 x (+.f64 2 x))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
1.0ms	(-.f64 x (+.f64 2 x))

rewrite19.0ms (0.6%)

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:

9.0ms	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
6.0ms	(-.f64 x (+.f64 2 x))

simplify72.0ms (2.2%)

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

prune85.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	125	5	130

Error

0.4b

Counts

130 → 5

Alt Table

Status	Error	Program
	35.4b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
▶	0.5b	(/.f64 -2 (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))))
	11.5b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 x (+.f64 2 x)) (-.f64 x (+.f64 2 x))) (-.f64 x (+.f64 2 x))) (.f64 (.f64 (fma.f64 x x -1) (fma.f64 x x -1)) (fma.f64 x x -1))))
	1.6b	(.f64 (.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))

Compiler

Compiled 2533 to 1743 computations (31.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.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))

rewrite5.0ms (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:

2.0ms

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

simplify59.0ms (1.8%)

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

prune34.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	48	5	53

Error

0.4b

Counts

53 → 5

Alt Table

Status	Error	Program
	35.4b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓	0.5b	(/.f64 -2 (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))))
	1.6b	(.f64 (.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
	8.4b	(cbrt.f64 (.f64 (.f64 (/.f64 -2 (fma.f64 x x -1)) (/.f64 -2 (fma.f64 x x -1))) (/.f64 -2 (fma.f64 x x -1))))

Compiler

Compiled 801 to 607 computations (24.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 -2 (cbrt.f64 (fma.f64 x x -1)))
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
✓	0.4b	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
✓	14.0b	(cbrt.f64 (fma.f64 x x -1))

series33.0ms (1%)

Counts

4 → 48

Calls

4 calls:

11.0ms	(/.f64 -2 (cbrt.f64 (fma.f64 x x -1)))
8.0ms	(cbrt.f64 (fma.f64 x x -1))
7.0ms	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
7.0ms	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.f64 1 (*.f64 (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)))
3.0ms	(/.f64 -2 (cbrt.f64 (fma.f64 x x -1)))
1.0ms	(cbrt.f64 (fma.f64 x x -1))

simplify135.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
499×	`associate-l_binary64`
417×	`fma-neg_binary64`
242×	`times-frac_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

181 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	3566
1	581	3284
2	1639	3053
3	4512	3042
4	4995	3042
5	4902	3042

prune318.0ms (9.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	292	5	297

Error

0.4b

Counts

297 → 5

Alt Table

Status	Error	Program
	35.4b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓	0.5b	(/.f64 -2 (fma.f64 x x -1))
	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1))))) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
	35.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (/.f64 -2 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))))
	8.4b	(cbrt.f64 (.f64 (.f64 (/.f64 -2 (fma.f64 x x -1)) (/.f64 -2 (fma.f64 x x -1))) (/.f64 -2 (fma.f64 x x -1))))

Compiler

Compiled 8335 to 6343 computations (23.9% saved)

regimes194.0ms (5.9%)

Accuracy

Total 0.1b remaining (12.7%)

Threshold costs 0.1b (12.7%)

Counts

93 → 1

Compiler

Compiled 4518 to 3420 computations (24.3% 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)

sample792.0ms (24%)

Algorithm

1×

intervals

Results

217.0ms	1944×	body	512	valid
177.0ms	4629×	body	128	valid
77.0ms	1015×	body	256	valid
58.0ms	412×	body	1024	valid

Compiler

Compiled 130 to 96 computations (26.2% 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

analyze5.0ms (0.1%)

sample84.0ms (2.5%)

simplify12.0ms (0.4%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series10.0ms (0.3%)

rewrite156.0ms (4.7%)

simplify623.0ms (18.9%)

prune603.0ms (18.3%)

localize6.0ms (0.2%)

series5.0ms (0.1%)

rewrite19.0ms (0.6%)

simplify72.0ms (2.2%)

prune85.0ms (2.6%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify59.0ms (1.8%)

prune34.0ms (1%)

localize8.0ms (0.2%)

series33.0ms (1%)

rewrite20.0ms (0.6%)

simplify135.0ms (4.1%)

prune318.0ms (9.7%)

regimes194.0ms (5.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample792.0ms (24%)

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