Details

analyze58.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample131.0ms (2.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
6.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify122.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1247×	`unsub-neg_binary64`
616×	`neg-sub0_binary64`
571×	`neg-mul-1_binary64`
560×	`fma-neg_binary64`
452×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	17
3	116	17
4	358	17
5	1331	17
6	3463	17
7	3625	17
8	4293	17
9	4678	17
10	4650	17
11	4895	17
12	4905	17

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

series32.0ms (0.7%)

Counts

3 → 68

Calls

3 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
39×	`prod-diff_binary64`
37×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 137

Calls

3 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify187.0ms (4%)

Algorithm

1×	egg-herbie

Rules

351×	`associate-/l/_binary64`
336×	`associate-/r*_binary64`
279×	`associate-+l+_binary64`
244×	`associate-/r/_binary64`
193×	`associate-l_binary64`

Counts

205 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	4112
1	462	3580
2	1832	3499
3	4716	3499
4	4995	3499
5	4924	3499

prune221.0ms (4.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	221	4	225

Error

Counts

225 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	2.6b	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))
▶	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 5577 to 3679 computations (34% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
✓	0.0b	(/.f64 v (-.f64 1 m))
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
✓	0.1b	(/.f64 m (/.f64 v (-.f64 1 m)))

series43.0ms (0.9%)

Counts

4 → 84

Calls

4 calls:

13.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
11.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
10.0ms	(/.f64 v (-.f64 1 m))
9.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)

rewrite183.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

684×	`times-frac_binary64`
597×	`add-sqr-sqrt_binary64`
563×	`*-un-lft-identity_binary64`
394×	`add-cube-cbrt_binary64`
249×	`prod-diff_binary64`

Counts

4 → 563

Calls

4 calls:

64.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
29.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
7.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
4.0ms	(/.f64 v (-.f64 1 m))

simplify436.0ms (9.4%)

Algorithm

1×	egg-herbie

Rules

425×	`fma-neg_binary64`
233×	`associate-/l*_binary64`
232×	`*-commutative_binary64`
213×	`associate-l_binary64`
213×	`associate-*l/_binary64`

Counts

647 → 768

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	422	14395
1	945	13545
2	3863	13035
3	4614	13035
4	4996	13035
5	4935	13035

prune888.0ms (19.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	768	0	768
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	768	4	772

Error

Counts

772 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	2.6b	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
▶	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 23030 to 15394 computations (33.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
✓	0.2b	(*.f64 (/.f64 m v) m)
✓	8.7b	(/.f64 (pow.f64 m 3) v)

series56.0ms (1.2%)

Counts

4 → 72

Calls

4 calls:

18.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
13.0ms	(/.f64 (pow.f64 m 3) v)
12.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
12.0ms	(*.f64 (/.f64 m v) m)

rewrite51.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
55×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 183

Calls

4 calls:

20.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
7.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
4.0ms	(*.f64 (/.f64 m v) m)
4.0ms	(/.f64 (pow.f64 m 3) v)

simplify139.0ms (3%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
301×	`cancel-sign-sub-inv_binary64`
264×	`unswap-sqr_binary64`
188×	`log-prod_binary64`
174×	`associate-r_binary64`

Counts

255 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	270	4662
1	552	4309
2	2340	3942
3	4392	3846
4	5016	3846

prune258.0ms (5.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	256	4	260

Error

Counts

260 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 (+.f64 m (/.f64 m v)) (.f64 (/.f64 (.f64 m m) v) (-.f64 m 2))) -1)
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 8320 to 3661 computations (56% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 m (/.f64 m v)) (.f64 (/.f64 (.f64 m m) v) (-.f64 m 2)))
✓	0.0b	(+.f64 m (/.f64 m v))
✓	0.1b	(.f64 (/.f64 (.f64 m m) v) (-.f64 m 2))
✓	14.5b	(/.f64 (*.f64 m m) v)

series110.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

66.0ms	(/.f64 (*.f64 m m) v)
20.0ms	(+.f64 (+.f64 m (/.f64 m v)) (.f64 (/.f64 (.f64 m m) v) (-.f64 m 2)))
17.0ms	(.f64 (/.f64 (.f64 m m) v) (-.f64 m 2))
6.0ms	(+.f64 m (/.f64 m v))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`associate-+r+_binary64`

Counts

4 → 157

Calls

4 calls:

11.0ms	(+.f64 (+.f64 m (/.f64 m v)) (.f64 (/.f64 (.f64 m m) v) (-.f64 m 2)))
9.0ms	(.f64 (/.f64 (.f64 m m) v) (-.f64 m 2))
4.0ms	(+.f64 m (/.f64 m v))
4.0ms	(/.f64 (*.f64 m m) v)

simplify142.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
454×	`fma-neg_binary64`
228×	`distribute-rgt-in_binary64`
220×	`associate-l_binary64`
216×	`distribute-lft-in_binary64`

Counts

253 → 241

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	291	4723
1	709	4022
2	2723	3867
3	4875	3865
4	5115	3865

prune239.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	241	4	245

Error

Counts

245 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 (+.f64 m (/.f64 m v)) (.f64 (/.f64 (.f64 m m) v) (-.f64 m 2))) -1)
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 7282 to 3333 computations (54.2% saved)

regimes386.0ms (8.3%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

Counts

134 → 1

Compiler

Compiled 7173 to 4944 computations (31.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	20	25
2	21	25
3	20	25

end1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

sample849.0ms (18.3%)

Algorithm

1×

intervals

Results

345.0ms	8000×	body	128	valid
172.0ms	8050×	pre	128	true
2.0ms	50×	body	128	invalid

Compiler

Compiled 117 to 79 computations (32.5% saved)

Details

analyze58.0ms (1.3%)

sample131.0ms (2.8%)

simplify122.0ms (2.6%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series32.0ms (0.7%)

rewrite36.0ms (0.8%)

simplify187.0ms (4%)

prune221.0ms (4.8%)

localize6.0ms (0.1%)

series43.0ms (0.9%)

rewrite183.0ms (3.9%)

simplify436.0ms (9.4%)

prune888.0ms (19.1%)

localize11.0ms (0.2%)

series56.0ms (1.2%)

rewrite51.0ms (1.1%)

simplify139.0ms (3%)

prune258.0ms (5.6%)

localize10.0ms (0.2%)

series110.0ms (2.4%)

rewrite40.0ms (0.9%)

simplify142.0ms (3.1%)

prune239.0ms (5.1%)

regimes386.0ms (8.3%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample849.0ms (18.3%)

Profiling