Details

analyze65.0ms (1.5%)

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)

sample1.2s (29.3%)

Results

931.0ms	8256×	body	128	valid
7.0ms	68×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify120.0ms (2.8%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(*.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)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
11.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite39.0ms (0.9%)

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

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
481×	`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	3059
1	413	2618
2	1688	2595
3	4507	2594
4	4922	2594

prune261.0ms (6.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	236	9	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	238	9	247

Error

Counts

247 → 9

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (/.f64 (.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v) 1) m)
	1.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
▶	0.3b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	1.7b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
	33.3b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	12.3b	(/.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))
	18.7b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	0.9b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)

Compiler

Compiled 5241 to 3194 computations (39.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series60.0ms (1.4%)

Counts

4 → 92

Calls

4 calls:

27.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
14.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
10.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
9.0ms	(-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1)

rewrite74.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`times-frac_binary64`
155×	`add-sqr-sqrt_binary64`
141×	`*-un-lft-identity_binary64`
123×	`add-cube-cbrt_binary64`
96×	`prod-diff_binary64`

Counts

4 → 289

Calls

4 calls:

15.0ms	(-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1)
15.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
7.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
7.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

simplify178.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-/l*_binary64`
432×	`distribute-rgt-in_binary64`
403×	`distribute-lft-in_binary64`
325×	`associate-/r/_binary64`
323×	`fma-def_binary64`

Counts

381 → 411

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	6616
1	468	5888
2	1524	5517
3	4740	5517
4	5001	5517

prune471.0ms (11.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	408	3	411
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	413	7	420

Error

Counts

420 → 7

Alt Table

Status	Error	Program
	9.6b	(.f64 (+.f64 (sqrt.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m))))) 1) (.f64 m (+.f64 -1 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)))))
	33.3b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	0.6b	(.f64 (.f64 (-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1) (sqrt.f64 m)) (sqrt.f64 m))
	0.3b	(.f64 (-.f64 (/.f64 (.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v) 1) m)
▶	0.2b	(*.f64 (+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) 0) m)
	18.7b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))

Compiler

Compiled 10773 to 7984 computations (25.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)
✓	0.2b	(*.f64 (+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) 0) m)

series18.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(*.f64 (+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) 0) m)
7.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 33

Calls

2 calls:

5.0ms	(*.f64 (+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) 0) m)
0.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify86.0ms (2%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-def_binary64`
573×	`fma-neg_binary64`
348×	`div-sub_binary64`
281×	`*-commutative_binary64`
258×	`associate-*l/_binary64`

Counts

81 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	1287
1	156	1118
2	453	1050
3	1435	1050
4	3323	1050
5	4280	1050
6	5050	1050

prune65.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	70	7	77

Error

Counts

77 → 7

Alt Table

Status	Error	Program
	9.6b	(.f64 (+.f64 (sqrt.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m))))) 1) (.f64 m (+.f64 -1 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)))))
	33.3b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	0.6b	(.f64 (.f64 (-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1) (sqrt.f64 m)) (sqrt.f64 m))
▶	0.3b	(.f64 (-.f64 (/.f64 (.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v) 1) m)
✓	0.2b	(*.f64 (+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) 0) m)
	18.7b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))

Compiler

Compiled 1512 to 925 computations (38.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series108.0ms (2.5%)

Counts

4 → 29

Calls

4 calls:

52.0ms	(.f64 (-.f64 (/.f64 (.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v) 1) m)
34.0ms	(/.f64 (*.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v)
15.0ms	(*.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m)))
6.0ms	(fma.f64 m (sqrt.f64 m) m)

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
27×	`sqrt-prod_binary64`

Counts

4 → 139

Calls

4 calls:

9.0ms	(.f64 (-.f64 (/.f64 (.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v) 1) m)
9.0ms	(*.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m)))
8.0ms	(/.f64 (*.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v)
0.0ms	(fma.f64 m (sqrt.f64 m) m)

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

905×	`times-frac_binary64`
561×	`distribute-rgt-in_binary64`
537×	`fma-def_binary64`
173×	`associate-l_binary64`
147×	`associate-r_binary64`

Counts

168 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	3932
1	428	3574
2	1646	3300
3	4979	3300

prune191.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	193	7	200

Error

Counts

200 → 7

Alt Table

Status	Error	Program
	0.4b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	0.6b	(.f64 (.f64 (-.f64 (/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m)))) 1) (sqrt.f64 m)) (sqrt.f64 m))
✓	0.3b	(.f64 (-.f64 (/.f64 (.f64 (fma.f64 m (sqrt.f64 m) m) (-.f64 1 (sqrt.f64 m))) v) 1) m)
	9.6b	(.f64 (+.f64 (sqrt.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m))))) 1) (.f64 m (+.f64 -1 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)))))
✓	0.2b	(*.f64 (+.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) 0) m)
	18.7b	(/.f64 (.f64 m (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3))) (+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (+.f64 (.f64 1 1) (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))))
	8.7b	(-.f64 (/.f64 (.f64 m (-.f64 m (.f64 m m))) v) m)

Compiler

Compiled 5531 to 2327 computations (57.9% saved)

regimes849.0ms (20%)

Accuracy

Total 0.2b remaining (87.2%)

Threshold costs 0.2b (87.2%)

Counts

249 → 1

Compiler

Compiled 16160 to 11499 computations (28.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	17	16
2	21	16
3	23	16
4	24	16
5	22	16

end104.0ms (2.5%)

Compiler: Compiled 178 to 120 computations (32.6% saved)

Details

analyze65.0ms (1.5%)

sample1.2s (29.3%)

simplify120.0ms (2.8%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series37.0ms (0.9%)

rewrite39.0ms (0.9%)

simplify104.0ms (2.5%)

prune261.0ms (6.1%)

localize8.0ms (0.2%)

series60.0ms (1.4%)

rewrite74.0ms (1.7%)

simplify178.0ms (4.2%)

prune471.0ms (11.1%)

localize7.0ms (0.2%)

series18.0ms (0.4%)

rewrite7.0ms (0.2%)

simplify86.0ms (2%)

prune65.0ms (1.5%)

localize9.0ms (0.2%)

series108.0ms (2.5%)

rewrite38.0ms (0.9%)

simplify91.0ms (2.1%)

prune191.0ms (4.5%)

regimes849.0ms (20%)

simplify2.0ms (0.1%)

end104.0ms (2.5%)

Profiling