Details

analyze92.0ms (2.2%)

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)

sample136.0ms (3.3%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify119.0ms (2.8%)

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

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 (/.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)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.8%)

Counts

4 → 80

Calls

4 calls:

15.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite88.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
57×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 188

Calls

4 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)
6.0ms	(*.f64 m (-.f64 1 m))

simplify139.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
345×	`associate-/r*_binary64`
257×	`associate-/r/_binary64`
250×	`associate-l_binary64`
225×	`exp-prod_binary64`

Counts

268 → 294

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4962
1	502	4321
2	2059	4004
3	4566	3999
4	5030	3999

prune336.0ms (8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	290	4	294
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	291	5	296

Error

Counts

296 → 5

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
	1.6b	(/.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 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 7235 to 4620 computations (36.1% saved)

localize12.0ms (0.3%)

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)
✓	9.5b	(/.f64 (pow.f64 m 3) v)

series58.0ms (1.4%)

Counts

4 → 72

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))
14.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1))
13.0ms	(/.f64 (pow.f64 m 3) v)
12.0ms	(*.f64 (/.f64 m v) m)

rewrite50.0ms (1.2%)

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:

19.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
8.0ms	(-.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)

simplify138.0ms (3.3%)

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

prune267.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	256	5	261

Error

Counts

261 → 5

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
▶	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
	0.2b	(*.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 8377 to 3702 computations (55.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 m (.f64 2 (.f64 m m)))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
✓	0.1b	(/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)
	9.5b	(/.f64 (pow.f64 m 3) v)

series38.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

18.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
17.0ms	(/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)
3.0ms	(-.f64 m (.f64 2 (.f64 m m)))

rewrite86.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
17×	`associate-+l+_binary64`
15×	`prod-diff_binary64`

Counts

3 → 98

Calls

3 calls:

72.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
4.0ms	(/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)
3.0ms	(-.f64 m (.f64 2 (.f64 m m)))

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

841×	`distribute-rgt-in_binary64`
817×	`distribute-lft-in_binary64`
668×	`fma-def_binary64`
134×	`cancel-sign-sub-inv_binary64`
101×	`fma-neg_binary64`

Counts

158 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	3117
1	449	2877
2	1470	2531
3	5623	2531

prune361.0ms (8.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	247	5	252

Error

Counts

252 → 5

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
▶	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 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))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
	0.1b	(+.f64 (-.f64 (+.f64 m (*.f64 (/.f64 (fma.f64 m -2 1) v) m)) 1) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 7102 to 4232 computations (40.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1)
✓	0.0b	(-.f64 m (pow.f64 m 2))
✓	0.0b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
✓	0.1b	(/.f64 (-.f64 m (pow.f64 m 2)) v)

series37.0ms (0.9%)

Counts

4 → 67

Calls

4 calls:

14.0ms	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
12.0ms	(/.f64 (-.f64 m (pow.f64 m 2)) v)
9.0ms	(-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1)
2.0ms	(-.f64 m (pow.f64 m 2))

rewrite118.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

264×	`add-sqr-sqrt_binary64`
197×	`*-un-lft-identity_binary64`
141×	`times-frac_binary64`
135×	`prod-diff_binary64`
135×	`add-cube-cbrt_binary64`

Counts

4 → 324

Calls

4 calls:

46.0ms	(/.f64 (-.f64 m (pow.f64 m 2)) v)
17.0ms	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
16.0ms	(-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1)
5.0ms	(-.f64 m (pow.f64 m 2))

simplify259.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

455×	`exp-prod_binary64`
271×	`times-frac_binary64`
248×	`fma-neg_binary64`
222×	`log-prod_binary64`
205×	`div-sub_binary64`

Counts

391 → 455

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	354	11333
1	652	7271
2	2281	6334
3	3874	6316
4	4576	6310
5	4822	6310

prune487.0ms (11.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	454	1	455
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	455	5	460

Error

Counts

460 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (*.f64 (/.f64 m v) m) 1)) (/.f64 (pow.f64 m 3) v))
	0.3b	(*.f64 (-.f64 (/.f64 (/.f64 (-.f64 m (pow.f64 m 2)) (sqrt.f64 v)) (sqrt.f64 v)) 1) (-.f64 1 m))
✓	0.1b	(*.f64 (-.f64 (/.f64 (-.f64 m (pow.f64 m 2)) v) 1) (-.f64 1 m))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 (-.f64 m (.f64 2 (.f64 m m))) v)) 1) (/.f64 (pow.f64 m 3) v))
	0.1b	(+.f64 (-.f64 (+.f64 m (*.f64 (/.f64 (fma.f64 m -2 1) v) m)) 1) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 12611 to 8258 computations (34.5% saved)

regimes318.0ms (7.6%)

Accuracy

Total 0.0b remaining (73.8%)

Threshold costs 0.0b (73.8%)

Counts

111 → 1

Compiler

Compiled 5514 to 3894 computations (29.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	21	26
2	22	26
3	20	26

end1.0ms (0%)

Compiler: Compiled 20 to 13 computations (35% saved)

sample911.0ms (21.7%)

Algorithm

1×

intervals

Results

358.0ms	8000×	body	128	valid
185.0ms	8067×	pre	128	true
3.0ms	67×	body	128	invalid

Compiler

Compiled 145 to 99 computations (31.7% saved)

Details

analyze92.0ms (2.2%)

sample136.0ms (3.3%)

simplify119.0ms (2.8%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series36.0ms (0.8%)

rewrite88.0ms (2.1%)

simplify139.0ms (3.3%)

prune336.0ms (8%)

localize12.0ms (0.3%)

series58.0ms (1.4%)

rewrite50.0ms (1.2%)

simplify138.0ms (3.3%)

prune267.0ms (6.4%)

localize11.0ms (0.3%)

series38.0ms (0.9%)

rewrite86.0ms (2%)

simplify78.0ms (1.9%)

prune361.0ms (8.6%)

localize8.0ms (0.2%)

series37.0ms (0.9%)

rewrite118.0ms (2.8%)

simplify259.0ms (6.2%)

prune487.0ms (11.6%)

regimes318.0ms (7.6%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample911.0ms (21.7%)

Profiling