Details

analyze72.0ms (2.8%)

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)

sample793.0ms (31.1%)

Results

756.0ms	8256×	body	128	valid
7.0ms	72×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify8.0ms (0.3%)

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 (0.1%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(*.f64 (fma.f64 x 3 -12/29) y)
▶	0.5b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 16 116))
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.5b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series9.0ms (0.3%)

Counts

3 → 48

Calls

3 calls:

6.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
1.0ms	(-.f64 x (/.f64 16 116))

rewrite31.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
48×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
38×	`times-frac_binary64`

Counts

3 → 118

Calls

3 calls:

8.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
8.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
6.0ms	(-.f64 x (/.f64 16 116))

simplify99.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-def_binary64`
591×	`times-frac_binary64`
420×	`associate-/l/_binary64`
297×	`*-commutative_binary64`
215×	`distribute-rgt-in_binary64`

Counts

166 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	241	1319
1	522	1059
2	1188	1053
3	2796	1052
4	4608	1052
5	4991	1052
6	3938	1052

prune156.0ms (6.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	167	8	175
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	169	8	177

Error

Counts

177 → 8

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (+.f64 x (.f64 (neg.f64 (/.f64 1 (.f64 (cbrt.f64 116) (cbrt.f64 116)))) (/.f64 16 (cbrt.f64 116)))) 3) y)
	0.5b	(*.f64 (fma.f64 3 x -12/29) y)
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	11.6b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	31.0b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))
	1.0b	(.f64 (.f64 (.f64 (-.f64 x 4/29) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)) y)
	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

Compiler

Compiled 3861 to 3210 computations (16.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
✓	0.1b	(*.f64 12/29 y)
✓	0.3b	(.f64 3 (.f64 y x))

series13.0ms (0.5%)

Counts

3 → 15

Calls

3 calls:

7.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
5.0ms	(.f64 3 (.f64 y x))
1.0ms	(*.f64 12/29 y)

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

4.0ms	(.f64 3 (.f64 y x))
4.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
3.0ms	(*.f64 12/29 y)

simplify77.0ms (3%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
509×	`associate-l_binary64`
472×	`fma-neg_binary64`
366×	`associate-r_binary64`
288×	`distribute-rgt-in_binary64`

Counts

71 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	701
1	230	632
2	626	623
3	1846	614
4	3688	612
5	4571	612
6	5558	612

prune71.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Error

Counts

93 → 7

Alt Table

Status	Error	Program
	11.6b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	31.0b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))
	0.5b	(*.f64 (fma.f64 3 x -12/29) y)
▶	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	1.0b	(.f64 (.f64 (.f64 (-.f64 x 4/29) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)) y)
	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	0.4b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (sqrt.f64 12/29) (.f64 (sqrt.f64 12/29) y)))

Compiler

Compiled 1334 to 882 computations (33.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (/.f64 16 116))
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite9.0ms (0.3%)

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:

7.0ms

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

simplify75.0ms (3%)

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

prune111.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	133	7	140

Error

Counts

140 → 7

Alt Table

Status	Error	Program
	11.6b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	31.0b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))
	0.5b	(*.f64 (fma.f64 3 x -12/29) y)
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	1.0b	(.f64 (.f64 (.f64 (-.f64 x 4/29) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)) y)
▶	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	0.4b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (sqrt.f64 12/29) (.f64 (sqrt.f64 12/29) y)))

Compiler

Compiled 3254 to 2735 computations (15.9% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x 4/29)
✓	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.4b	(.f64 3 (.f64 y (-.f64 x 4/29)))

series13.0ms (0.5%)

Counts

3 → 31

Calls

3 calls:

6.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
5.0ms	(*.f64 y (-.f64 x 4/29))
1.0ms	(-.f64 x 4/29)

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
63×	`prod-diff_binary64`
62×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`

Counts

3 → 154

Calls

3 calls:

7.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
6.0ms	(*.f64 y (-.f64 x 4/29))
3.0ms	(-.f64 x 4/29)

simplify93.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
499×	`neg-mul-1_binary64`
303×	`*-commutative_binary64`
245×	`distribute-rgt-neg-out_binary64`
242×	`distribute-lft-neg-out_binary64`

Counts

185 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2017
1	312	1518
2	753	1518
3	1781	1515
4	3712	1515
5	4915	1515

prune156.0ms (6.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	213	7	220

Error

Counts

220 → 7

Alt Table

Status	Error	Program
	11.6b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
	31.0b	(.f64 (.f64 (*.f64 (-.f64 x (/.f64 16 116)) 3) (sqrt.f64 y)) (sqrt.f64 y))
	0.5b	(*.f64 (fma.f64 3 x -12/29) y)
✓	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	1.0b	(.f64 (.f64 (.f64 (-.f64 x 4/29) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)) y)
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
	0.4b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (sqrt.f64 12/29) (.f64 (sqrt.f64 12/29) y)))

Compiler

Compiled 3876 to 2987 computations (22.9% saved)

regimes596.0ms (23.4%)

Accuracy

Total 0.2b remaining (94%)

Threshold costs 0.2b (94%)

Counts

115 → 1

Compiler

Compiled 8655 to 6865 computations (20.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end89.0ms (3.5%)

Compiler: Compiled 110 to 85 computations (22.7% saved)

Details

analyze72.0ms (2.8%)

sample793.0ms (31.1%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite31.0ms (1.2%)

simplify99.0ms (3.9%)

prune156.0ms (6.1%)

localize6.0ms (0.2%)

series13.0ms (0.5%)

rewrite13.0ms (0.5%)

simplify77.0ms (3%)

prune71.0ms (2.8%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite9.0ms (0.3%)

simplify75.0ms (3%)

prune111.0ms (4.4%)

localize5.0ms (0.2%)

series13.0ms (0.5%)

rewrite29.0ms (1.1%)

simplify93.0ms (3.7%)

prune156.0ms (6.1%)

regimes596.0ms (23.4%)

simplify2.0ms (0.1%)

end89.0ms (3.5%)

Profiling