Details

analyze80.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
50%	50%	0.1%	6
62.4%	31.2%	6.3%	7
71.8%	21.9%	6.3%	8
76.5%	14%	9.5%	9
80.4%	10.1%	9.5%	10
82.3%	6.6%	11%	11
84.1%	4.9%	11%	12
85%	3.2%	11.8%	13
85.8%	2.4%	11.8%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample17.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 25 to 21 computations (16% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
13×	`distribute-lft-in_binary64`
13×	`distribute-rgt-in_binary64`
10×	`*-commutative_binary64`
9×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	18	10
2	32	8
3	56	8
4	68	8
5	74	8
6	66	8

prune3.0ms (0.2%)

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
	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
▶	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series7.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

6.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

rewrite18.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

9.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
7.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

simplify104.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
495×	`associate-r_binary64`
206×	`sqr-pow_binary64`
195×	`distribute-rgt-in_binary64`
194×	`distribute-lft-in_binary64`

Counts

83 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	921
1	206	672
2	611	666
3	1677	666
4	2385	666
5	3622	666
6	4778	666
7	4997	666
8	4869	666

prune63.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	81	6	87

Error

Counts

87 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	30.7b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))
▶	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	13.2b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	17.3b	(/.f64 (.f64 y (fma.f64 3 (pow.f64 x 3) -192/24389)) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 16 116) (/.f64 16 116)) (.f64 x (/.f64 16 116)))))
	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

Compiler

Compiled 1369 to 1067 computations (22.1% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(*.f64 (-.f64 x (/.f64 16 116)) (*.f64 3 y))

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`

Counts

1 → 25

Calls

1 calls:

8.0ms

(*.f64 (-.f64 x (/.f64 16 116)) (*.f64 3 y))

simplify76.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
545×	`associate-l_binary64`
389×	`associate-r_binary64`
207×	`unswap-sqr_binary64`
175×	`fma-neg_binary64`

Counts

49 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	656
1	172	447
2	499	447
3	1627	443
4	2444	443
5	3664	443
6	4975	443
7	4985	443

prune33.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	43	6	49

Error

Counts

49 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	30.7b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	13.2b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	17.3b	(/.f64 (.f64 y (fma.f64 3 (pow.f64 x 3) -192/24389)) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 16 116) (/.f64 16 116)) (.f64 x (/.f64 16 116)))))
▶	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

Compiler

Compiled 796 to 622 computations (21.9% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

series16.0ms (0.8%)

Counts

2 → 28

Calls

2 calls:

8.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
8.0ms	(*.f64 y (-.f64 x 4/29))

rewrite54.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

15.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
10.0ms	(*.f64 y (-.f64 x 4/29))

simplify103.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
474×	`*-commutative_binary64`
412×	`unsub-neg_binary64`
391×	`neg-mul-1_binary64`
389×	`neg-sub0_binary64`

Counts

152 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	1710
1	293	1349
2	721	1349
3	1730	1347
4	3194	1347
5	4989	1347
6	4900	1347

prune130.0ms (6.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	166	6	172

Error

Counts

172 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	30.7b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
▶	13.2b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	17.3b	(/.f64 (.f64 y (fma.f64 3 (pow.f64 x 3) -192/24389)) (+.f64 (.f64 x x) (+.f64 (.f64 4/29 4/29) (.f64 x 4/29))))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

Compiler

Compiled 3239 to 2500 computations (22.8% saved)

localize19.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x -16/841)
✓	0.7b	(*.f64 3 (fma.f64 x x -16/841))
✓	4.9b	(.f64 y (.f64 3 (fma.f64 x x -16/841)))
✓	7.5b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))

series45.0ms (2.3%)

Counts

4 → 72

Calls

4 calls:

20.0ms	(.f64 y (.f64 3 (fma.f64 x x -16/841)))
20.0ms	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
3.0ms	(*.f64 3 (fma.f64 x x -16/841))
2.0ms	(fma.f64 x x -16/841)

rewrite26.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(*.f64 3 (fma.f64 x x -16/841))
8.0ms	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
4.0ms	(.f64 y (.f64 3 (fma.f64 x x -16/841)))
0.0ms	(fma.f64 x x -16/841)

simplify120.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-def_binary64`
437×	`associate-*l/_binary64`
361×	`distribute-rgt-in_binary64`
358×	`distribute-lft-in_binary64`
350×	`associate-/r*_binary64`

Counts

157 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2162
1	326	1901
2	1203	1864
3	4693	1846
4	5336	1846

prune98.0ms (5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	1	2
Picked	1	0	1
Done	0	3	3
Total	145	5	150

Error

Counts

150 → 5

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	13.1b	(/.f64 (.f64 y (-.f64 (.f64 3 (pow.f64 x 2)) 48/841)) (+.f64 x (/.f64 16 116)))
	17.3b	(/.f64 (.f64 y (fma.f64 3 (pow.f64 x 3) -192/24389)) (+.f64 (.f64 x x) (+.f64 (.f64 4/29 4/29) (.f64 x 4/29))))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 2770 to 2020 computations (27.1% saved)

regimes316.0ms (16.3%)

Accuracy

Total 0.2b remaining (92.7%)

Threshold costs 0.2b (92.7%)

Counts

58 → 1

Compiler

Compiled 4265 to 3346 computations (21.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	13	10
2	14	10
3	13	10

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample574.0ms (29.5%)

Algorithm

1×

intervals

Results

299.0ms	8000×	body	128	valid
3.0ms	80×	body	128	invalid

Compiler

Compiled 93 to 75 computations (19.4% saved)

Details

analyze80.0ms (4.1%)

sample17.0ms (0.9%)

simplify9.0ms (0.4%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite18.0ms (0.9%)

simplify104.0ms (5.3%)

prune63.0ms (3.2%)

localize6.0ms (0.3%)

series7.0ms (0.3%)

rewrite9.0ms (0.5%)

simplify76.0ms (3.9%)

prune33.0ms (1.7%)

localize4.0ms (0.2%)

series16.0ms (0.8%)

rewrite54.0ms (2.8%)

simplify103.0ms (5.3%)

prune130.0ms (6.7%)

localize19.0ms (1%)

series45.0ms (2.3%)

rewrite26.0ms (1.3%)

simplify120.0ms (6.2%)

prune98.0ms (5%)

regimes316.0ms (16.3%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample574.0ms (29.5%)

Profiling