Details

analyze87.0ms (2.4%)

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 26 to 19 computations (26.9% saved)

sample1.2s (33.2%)

Results

1.1s	8256×	body	128	valid
7.0ms	56×	body	128	invalid

Compiler

Compiled 67 to 49 computations (26.9% saved)

simplify120.0ms (3.3%)

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

0.1b

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 2 expressions with local error:

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

series22.0ms (0.6%)

Counts

2 → 44

Calls

2 calls:

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

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 86

Calls

2 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)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
771×	`distribute-rgt-in_binary64`
719×	`distribute-lft-in_binary64`
185×	`associate-l_binary64`
144×	`associate-r_binary64`

Counts

130 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3001
1	424	2861
2	1772	2609
3	5141	2609

prune139.0ms (3.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	147	3	150

Error

Counts

150 → 3

Alt Table

Status	Error	Program
	0.1b	(.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 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
	3.3b	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))

Compiler

Compiled 3732 to 2337 computations (37.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
✓	7.9b	(/.f64 (pow.f64 m 3) v)
✓	13.5b	(/.f64 (*.f64 m m) v)

series59.0ms (1.6%)

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)
14.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
11.0ms	(/.f64 (*.f64 m m) v)

rewrite53.0ms (1.5%)

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:

24.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
8.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
4.0ms	(/.f64 (pow.f64 m 3) v)
4.0ms	(/.f64 (*.f64 m m) v)

simplify132.0ms (3.7%)

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

prune215.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	229	3	232

Error

Counts

232 → 3

Alt Table

Status	Error	Program
▶	0.1b	(.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 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
	3.3b	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))

Compiler

Compiled 7589 to 3385 computations (55.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series75.0ms (2.1%)

Counts

3 → 28

Calls

3 calls:

42.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
27.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
6.0ms	(-.f64 1 (sqrt.f64 m))

rewrite57.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
54×	`prod-diff_binary64`
49×	`add-cube-cbrt_binary64`
43×	`sqrt-prod_binary64`

Counts

3 → 184

Calls

3 calls:

20.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
4.0ms	(-.f64 1 (sqrt.f64 m))

simplify270.0ms (7.5%)

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

212 → 255

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	7869
1	749	7205
2	3280	6517
3	4804	6514
4	4895	6514

prune288.0ms (8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	302	0	302
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	302	3	305

Error

Counts

305 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.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 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
▶	3.3b	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))

Compiler

Compiled 10941 to 6452 computations (41% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 m m))
✓	0.1b	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m)))
✓	0.1b	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)
✓	3.0b	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))

series61.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

31.0ms	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))
19.0ms	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m)))
7.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)
2.0ms	(-.f64 1 (*.f64 m m))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 95

Calls

4 calls:

7.0ms	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))
5.0ms	(.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m)))
2.0ms	(-.f64 1 (*.f64 m m))
0.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify120.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

500×	`distribute-rgt-in_binary64`
469×	`fma-def_binary64`
457×	`distribute-lft-in_binary64`
267×	`associate-/l/_binary64`
229×	`associate-/r/_binary64`

Counts

179 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	4374
1	460	3905
2	1642	3654
3	4603	3645
4	5000	3645

prune162.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	189	3	192

Error

Counts

192 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.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 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
✓	3.3b	(/.f64 (.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1) (-.f64 1 (.f64 m m))) (+.f64 1 m))

Compiler

Compiled 4745 to 2758 computations (41.9% saved)

regimes300.0ms (8.4%)

Accuracy

Total 0.0b remaining (66.3%)

Threshold costs 0.0b (66.3%)

Counts

109 → 1

Compiler

Compiled 5482 to 3854 computations (29.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	21	29
2	25	29
3	27	29
4	28	29
5	27	29

end69.0ms (1.9%)

Compiler: Compiled 107 to 71 computations (33.6% saved)

Details

analyze87.0ms (2.4%)

sample1.2s (33.2%)

simplify120.0ms (3.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series22.0ms (0.6%)

rewrite27.0ms (0.7%)

simplify75.0ms (2.1%)

prune139.0ms (3.9%)

localize13.0ms (0.4%)

series59.0ms (1.6%)

rewrite53.0ms (1.5%)

simplify132.0ms (3.7%)

prune215.0ms (6%)

localize11.0ms (0.3%)

series75.0ms (2.1%)

rewrite57.0ms (1.6%)

simplify270.0ms (7.5%)

prune288.0ms (8%)

localize11.0ms (0.3%)

series61.0ms (1.7%)

rewrite20.0ms (0.5%)

simplify120.0ms (3.3%)

prune162.0ms (4.5%)

regimes300.0ms (8.4%)

simplify3.0ms (0.1%)

end69.0ms (1.9%)

Profiling