Details

analyze64.0ms (1.8%)

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 (34.1%)

Results

925.0ms	8256×	body	128	valid
6.0ms	52×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify119.0ms (3.3%)

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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series26.0ms (0.7%)

Counts

3 → 56

Calls

3 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
4.0ms	(*.f64 m (-.f64 1 m))

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 102

Calls

3 calls:

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

simplify89.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
346×	`associate-/l/_binary64`
288×	`fma-neg_binary64`

Counts

158 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	2119
1	364	1923
2	1597	1729
3	4495	1728
4	4950	1728

prune173.0ms (4.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Error

0.0b

Counts

171 → 7

Alt Table

Status	Error	Program
	15.9b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	0.3b	(.f64 (-.f64 (/.f64 (.f64 (*.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v) 1) m)
	22.7b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.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))))
	39.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.7b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m))))) 1) m)
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3519 to 1995 computations (43.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series20.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

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

simplify101.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-def_binary64`
343×	`div-sub_binary64`
334×	`fma-neg_binary64`
281×	`associate-*l/_binary64`
258×	`exp-prod_binary64`

Counts

80 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	1280
1	137	1054
2	376	1024
3	1249	1024
4	2963	1024
5	4675	1024
6	4979	1024
7	4930	1024

prune58.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	60	8	68

Error

Counts

68 → 8

Alt Table

Status	Error	Program
	39.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	22.7b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.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))))
	0.6b	(.f64 (sqrt.f64 m) (.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	15.9b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
▶	0.3b	(.f64 (-.f64 (/.f64 (.f64 (*.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v) 1) m)
	0.7b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m))))) 1) m)
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 1228 to 777 computations (36.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series71.0ms (2%)

Counts

4 → 35

Calls

4 calls:

28.0ms	(/.f64 (.f64 (.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v)
19.0ms	(.f64 (-.f64 (/.f64 (.f64 (*.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v) 1) m)
16.0ms	(.f64 (.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
7.0ms	(*.f64 m (+.f64 1 (sqrt.f64 m)))

rewrite58.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
28×	`sqrt-prod_binary64`

Counts

4 → 169

Calls

4 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 (*.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v) 1) m)
12.0ms	(/.f64 (.f64 (.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v)
11.0ms	(.f64 (.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
5.0ms	(*.f64 m (+.f64 1 (sqrt.f64 m)))

simplify146.0ms (4%)

Algorithm

1×	egg-herbie

Rules

532×	`fma-neg_binary64`
419×	`associate-/l/_binary64`
417×	`associate-l_binary64`
353×	`associate-r_binary64`
182×	`distribute-rgt-in_binary64`

Counts

204 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	4926
1	627	4401
2	2977	3526
3	4780	3526
4	5062	3526

prune283.0ms (7.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	238	8	246

Error

Counts

246 → 8

Alt Table

Status	Error	Program
	39.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	22.7b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.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))))
▶	0.6b	(.f64 (sqrt.f64 m) (.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	15.9b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.3b	(.f64 (-.f64 (/.f64 (.f64 (*.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v) 1) m)
	0.7b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m))))) 1) m)
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 7234 to 3789 computations (47.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.2b	(*.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.5b	(.f64 (sqrt.f64 m) (.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))

series38.0ms (1.1%)

Counts

2 → 32

Calls

2 calls:

22.0ms	(*.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
17.0ms	(.f64 (sqrt.f64 m) (.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 53

Calls

2 calls:

6.0ms	(.f64 (sqrt.f64 m) (.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))
4.0ms	(*.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

simplify103.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-def_binary64`
542×	`fma-neg_binary64`
408×	`*-commutative_binary64`
286×	`exp-prod_binary64`
243×	`div-sub_binary64`

Counts

85 → 86

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1759
1	215	1469
2	626	1385
3	1950	1379
4	3676	1343
5	4739	1343
6	4951	1343

prune86.0ms (2.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	108	8	116

Error

Counts

116 → 8

Alt Table

Status	Error	Program
	39.0b	(.f64 (sqrt.f64 (.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))) (sqrt.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	22.7b	(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) (pow.f64 1 3)) m) (+.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))))
✓	0.6b	(.f64 (sqrt.f64 m) (.f64 (sqrt.f64 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))
	6.8b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	15.9b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.3b	(.f64 (-.f64 (/.f64 (.f64 (*.f64 m (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m))) v) 1) m)
	0.7b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m))))) 1) m)
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 2179 to 1197 computations (45.1% saved)

regimes732.0ms (20.3%)

Accuracy

Total 0.2b remaining (89.3%)

Threshold costs 0.2b (89.3%)

Counts

227 → 1

Compiler

Compiled 13724 to 9042 computations (34.1% saved)

simplify3.0ms (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

end133.0ms (3.7%)

Compiler: Compiled 222 to 155 computations (30.2% saved)

Details

analyze64.0ms (1.8%)

sample1.2s (34.1%)

simplify119.0ms (3.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series26.0ms (0.7%)

rewrite27.0ms (0.8%)

simplify89.0ms (2.5%)

prune173.0ms (4.8%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify101.0ms (2.8%)

prune58.0ms (1.6%)

localize10.0ms (0.3%)

series71.0ms (2%)

rewrite58.0ms (1.6%)

simplify146.0ms (4%)

prune283.0ms (7.8%)

localize8.0ms (0.2%)

series38.0ms (1.1%)

rewrite12.0ms (0.3%)

simplify103.0ms (2.8%)

prune86.0ms (2.4%)

regimes732.0ms (20.3%)

simplify3.0ms (0.1%)

end133.0ms (3.7%)

Profiling