Details

analyze57.0ms (1.4%)

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 24 to 17 computations (29.2% saved)

sample310.0ms (7.7%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify117.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (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))
✓	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series36.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
10.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 153

Calls

4 calls:

9.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(*.f64 m (-.f64 1 m))

simplify106.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
482×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
328×	`fma-neg_binary64`
240×	`associate-l_binary64`

Counts

233 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3371
1	413	2852
2	1688	2595
3	4507	2594
4	4922	2594

prune214.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	239	8	247

Error

0.0b

Counts

247 → 8

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	31.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	0.4b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	14.8b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	8.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	45.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
	14.7b	(.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (-.f64 m (.f64 m m)) 3)) v) 1) m)

Compiler

Compiled 5076 to 3087 computations (39.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.2b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

series27.0ms (0.7%)

Counts

3 → 64

Calls

3 calls:

13.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
6.0ms	(/.f64 (-.f64 1 m) v)

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

3 → 76

Calls

3 calls:

6.0ms	(/.f64 (-.f64 1 m) v)
3.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify94.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
332×	`distribute-rgt-neg-out_binary64`
307×	`associate-l_binary64`
305×	`div-sub_binary64`
264×	`exp-prod_binary64`

Counts

140 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2018
1	285	1760
2	745	1726
3	2553	1726
4	4478	1726
5	4976	1726

prune106.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	127	8	135

Error

0.0b

Counts

135 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	31.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
▶	0.4b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	14.8b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	8.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	45.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
	14.7b	(.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (-.f64 m (.f64 m m)) 3)) v) 1) m)

Compiler

Compiled 2205 to 1336 computations (39.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
✓	0.3b	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))
✓	0.4b	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))

series94.0ms (2.3%)

Counts

3 → 52

Calls

3 calls:

40.0ms	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
32.0ms	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))
22.0ms	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))

rewrite51.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
72×	`add-sqr-sqrt_binary64`
63×	`sqrt-prod_binary64`
57×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`

Counts

3 → 158

Calls

3 calls:

22.0ms	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
8.0ms	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))

simplify130.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-/r*_binary64`
505×	`associate-*r/_binary64`
392×	`associate-/r/_binary64`
323×	`distribute-rgt-in_binary64`
310×	`distribute-lft-in_binary64`

Counts

210 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	4321
1	516	3995
2	1637	3840
3	4722	3840
4	4961	3840

prune251.0ms (6.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	307	8	315

Error

0.0b

Counts

315 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	31.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
✓	0.4b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	14.8b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	8.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	45.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
▶	0.6b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))) (sqrt.f64 v)) 1) m)

Compiler

Compiled 7364 to 3584 computations (51.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))
✓	0.4b	(*.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v))))
✓	0.4b	(/.f64 (*.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))) (sqrt.f64 v))
✓	0.7b	(cbrt.f64 v)

series262.0ms (6.5%)

Counts

4 → 72

Calls

4 calls:

114.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))
81.0ms	(/.f64 (*.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))) (sqrt.f64 v))
40.0ms	(cbrt.f64 v)
27.0ms	(*.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v))))

rewrite74.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`add-sqr-sqrt_binary64`
149×	`times-frac_binary64`
138×	`*-un-lft-identity_binary64`
90×	`sqrt-prod_binary64`
81×	`add-cube-cbrt_binary64`

Counts

4 → 251

Calls

4 calls:

25.0ms	(*.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v))))
13.0ms	(/.f64 (*.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))) (sqrt.f64 v))
7.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))
1.0ms	(cbrt.f64 v)

simplify188.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

370×	`div-sub_binary64`
279×	`associate-/l*_binary64`
252×	`times-frac_binary64`
250×	`distribute-rgt-in_binary64`
233×	`associate-*r/_binary64`

Counts

323 → 375

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	7027
1	758	6311
2	3137	5940
3	4452	5456
4	5339	5456

prune318.0ms (7.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	393	8	401

Error

0.0b

Counts

401 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	31.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
✓	0.4b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	14.8b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	8.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	45.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
✓	0.6b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (cbrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 (cbrt.f64 v)))) (sqrt.f64 v)) 1) m)

Compiler

Compiled 10859 to 5079 computations (53.2% saved)

regimes545.0ms (13.6%)

Accuracy

Total 0.2b remaining (84.7%)

Threshold costs 0.2b (84.7%)

Counts

98 → 1

Compiler

Compiled 5289 to 3553 computations (32.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	16	14
2	19	14
3	21	14
4	22	14
5	21	14

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample948.0ms (23.6%)

Algorithm

1×

intervals

Results

382.0ms	8000×	body	128	valid
186.0ms	8056×	pre	128	true
2.0ms	56×	body	128	invalid

Compiler

Compiled 172 to 112 computations (34.9% saved)

Details

analyze57.0ms (1.4%)

sample310.0ms (7.7%)

simplify117.0ms (2.9%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series36.0ms (0.9%)

rewrite41.0ms (1%)

simplify106.0ms (2.6%)

prune214.0ms (5.3%)

localize6.0ms (0.1%)

series27.0ms (0.7%)

rewrite12.0ms (0.3%)

simplify94.0ms (2.3%)

prune106.0ms (2.6%)

localize8.0ms (0.2%)

series94.0ms (2.3%)

rewrite51.0ms (1.3%)

simplify130.0ms (3.2%)

prune251.0ms (6.2%)

localize11.0ms (0.3%)

series262.0ms (6.5%)

rewrite74.0ms (1.8%)

simplify188.0ms (4.7%)

prune318.0ms (7.9%)

regimes545.0ms (13.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample948.0ms (23.6%)

Profiling