Details

analyze89.0ms (2.7%)

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)

sample138.0ms (4.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify123.0ms (3.8%)

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

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series27.0ms (0.8%)

Counts

3 → 56

Calls

3 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`distribute-lft-in_binary64`

Counts

3 → 137

Calls

3 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify171.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

806×	`distribute-rgt-in_binary64`
733×	`distribute-lft-in_binary64`
365×	`fma-neg_binary64`
242×	`associate-l_binary64`
195×	`associate-r_binary64`

Counts

193 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	3683
1	464	3476
2	1999	3134
3	4909	3134
4	5060	3134

prune208.0ms (6.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	218	3	221

Error

Counts

221 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
▶	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
	0.1b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

Compiler

Compiled 5332 to 3215 computations (39.7% saved)

localize11.0ms (0.4%)

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 m) v) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
✓	8.1b	(/.f64 (pow.f64 m 3) v)
✓	10.9b	(/.f64 (*.f64 m m) v)

series58.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

19.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
15.0ms	(/.f64 (pow.f64 m 3) v)
13.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
11.0ms	(/.f64 (*.f64 m m) v)

rewrite69.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
49×	`add-cube-cbrt_binary64`
39×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 172

Calls

4 calls:

37.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
7.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
4.0ms	(/.f64 (pow.f64 m 3) v)
3.0ms	(/.f64 (*.f64 m m) v)

simplify138.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/l/_binary64`
458×	`fma-neg_binary64`
451×	`unswap-sqr_binary64`
187×	`cancel-sign-sub-inv_binary64`
136×	`associate-/l*_binary64`

Counts

244 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	4559
1	487	4206
2	2089	3968
3	4854	3968
4	5037	3968

prune206.0ms (6.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	229	3	232

Error

Counts

232 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
▶	0.1b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

Compiler

Compiled 7606 to 3396 computations (55.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series69.0ms (2.1%)

Counts

2 → 27

Calls

2 calls:

44.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
25.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
36×	`prod-diff_binary64`
33×	`add-cube-cbrt_binary64`
32×	`frac-times_binary64`

Counts

2 → 138

Calls

2 calls:

20.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
11.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))

simplify184.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

455×	`associate-l_binary64`
387×	`associate-r_binary64`
385×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
338×	`fma-neg_binary64`

Counts

165 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	7280
1	740	6708
2	3262	6110
3	4763	6089
4	4987	6089

prune423.0ms (12.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	325	0	325
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	325	3	328

Error

Counts

328 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.1b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

Compiler

Compiled 11469 to 6773 computations (40.9% saved)

regimes319.0ms (9.8%)

Accuracy

Total 0.0b remaining (68.9%)

Threshold costs 0.0b (68.9%)

Counts

102 → 1

Compiler

Compiled 5484 to 3888 computations (29.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`distribute-lft-neg-in_binary64`
3×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	25	28
2	32	28
3	39	28
4	44	28
5	47	28
6	48	28
7	47	28

end1.0ms (0%)

Compiler: Compiled 21 to 14 computations (33.3% saved)

sample926.0ms (28.3%)

Algorithm

1×

intervals

Results

380.0ms	8000×	body	128	valid
186.0ms	8049×	pre	128	true
2.0ms	49×	body	128	invalid

Compiler

Compiled 107 to 75 computations (29.9% saved)

Details

analyze89.0ms (2.7%)

sample138.0ms (4.2%)

simplify123.0ms (3.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series27.0ms (0.8%)

rewrite35.0ms (1.1%)

simplify171.0ms (5.2%)

prune208.0ms (6.4%)

localize11.0ms (0.4%)

series58.0ms (1.8%)

rewrite69.0ms (2.1%)

simplify138.0ms (4.2%)

prune206.0ms (6.3%)

localize11.0ms (0.3%)

series69.0ms (2.1%)

rewrite50.0ms (1.5%)

simplify184.0ms (5.6%)

prune423.0ms (12.9%)

regimes319.0ms (9.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample926.0ms (28.3%)

Profiling