Details

analyze8.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.6s (36%)

Results

473.0ms	4650×	body	128	valid
450.0ms	1276×	body	1024	valid
442.0ms	1562×	body	512	valid
175.0ms	768×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

6.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	1.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series10.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (+.f64 x 1))
2.0ms	(/.f64 1 (-.f64 x 1))

rewrite190.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

757×	`*-un-lft-identity_binary64`
733×	`times-frac_binary64`
558×	`add-sqr-sqrt_binary64`
508×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

4 → 668

Calls

4 calls:

45.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
17.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify451.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
457×	`times-frac_binary64`
236×	`fma-def_binary64`
186×	`sub-neg_binary64`
176×	`exp-prod_binary64`

Counts

716 → 853

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	19278
1	989	13709
2	2519	9843
3	4349	9843
4	4815	9843

prune795.0ms (18.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	851	2	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	851	3	854

Error

0.0b

Counts

854 → 3

Alt Table

Status	Error	Program
▶	25.1b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
	38.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
✓	6.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 33619 to 26159 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
✓	0.0b	(+.f64 x (pow.f64 x 3))

series7.0ms (0.2%)

Counts

2 → 18

Calls

2 calls:

5.0ms	(+.f64 x (pow.f64 x 3))
3.0ms	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 29

Calls

2 calls:

4.0ms	(+.f64 x (pow.f64 x 3))
0.0ms	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

815×	`distribute-rgt-in_binary64`
643×	`fma-neg_binary64`
264×	`cancel-sign-sub-inv_binary64`
264×	`exp-prod_binary64`
217×	`distribute-rgt-out_binary64`

Counts

47 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	55	577
1	143	498
2	420	496
3	1584	494
4	4485	493
5	4990	493
6	4959	493
7	4944	493

prune39.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	53	3	56

Error

0.0b

Counts

56 → 3

Alt Table

Status	Error	Program
✓	25.1b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
▶	38.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
✓	6.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 831 to 605 computations (27.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9))))
✓	0.1b	(/.f64 2 (pow.f64 x 3))
✓	0.2b	(/.f64 2 (pow.f64 x 5))
✓	0.3b	(/.f64 2 (pow.f64 x 7))

series15.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 2 (pow.f64 x 7))
4.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9))))
3.0ms	(/.f64 2 (pow.f64 x 5))
3.0ms	(/.f64 2 (pow.f64 x 3))

rewrite70.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
92×	`*-un-lft-identity_binary64`
78×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
45×	`unpow-prod-down_binary64`

Counts

4 → 210

Calls

4 calls:

48.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9))))
4.0ms	(/.f64 2 (pow.f64 x 3))
3.0ms	(/.f64 2 (pow.f64 x 7))
3.0ms	(/.f64 2 (pow.f64 x 5))

simplify131.0ms (3%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
379×	`distribute-rgt-in_binary64`
260×	`fma-neg_binary64`
223×	`cancel-sign-sub-inv_binary64`
205×	`unswap-sqr_binary64`

Counts

222 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	3445
1	619	3345
2	2167	3247
3	4817	3247
4	4944	3247

prune236.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	248	4	252

Error

Counts

252 → 4

Alt Table

Status	Error	Program
✓	25.1b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
✓	38.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
✓	6.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	38.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 7988 to 6589 computations (17.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9))))
✓	0.1b	(/.f64 (/.f64 2 x) (*.f64 x x))
	0.2b	(/.f64 2 (pow.f64 x 5))
	0.3b	(/.f64 2 (pow.f64 x 7))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9))))
3.0ms	(/.f64 (/.f64 2 x) (*.f64 x x))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
25×	`fma-def_binary64`

Counts

2 → 93

Calls

2 calls:

29.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9))))
5.0ms	(/.f64 (/.f64 2 x) (*.f64 x x))

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Rules

633×	`fma-def_binary64`
615×	`times-frac_binary64`
358×	`distribute-rgt-in_binary64`
328×	`fma-neg_binary64`
320×	`distribute-lft-in_binary64`

Counts

117 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	1786
1	486	1702
2	1709	1643
3	4975	1643
4	5149	1643

prune220.0ms (5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	248	4	252

Error

Counts

252 → 4

Alt Table

Status	Error	Program
✓	25.1b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
✓	38.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
✓	6.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	38.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 (/.f64 2 x) (*.f64 x x)) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 8365 to 6248 computations (25.3% saved)

regimes132.0ms (3%)

Accuracy

Total 0.7b remaining (95.6%)

Threshold costs 0.7b (95.6%)

Counts

37 → 3

Compiler

Compiled 1518 to 1240 computations (18.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	124
1	59	124
2	67	124
3	70	124
4	71	124
5	68	124

end198.0ms (4.5%)

Compiler: Compiled 245 to 197 computations (19.6% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze8.0ms (0.2%)

sample1.6s (36%)

simplify16.0ms (0.4%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

series10.0ms (0.2%)

rewrite190.0ms (4.3%)

simplify451.0ms (10.3%)

prune795.0ms (18.2%)

localize6.0ms (0.1%)

series7.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify91.0ms (2.1%)

prune39.0ms (0.9%)

localize13.0ms (0.3%)

series15.0ms (0.3%)

rewrite70.0ms (1.6%)

simplify131.0ms (3%)

prune236.0ms (5.4%)

localize13.0ms (0.3%)

series10.0ms (0.2%)

rewrite41.0ms (0.9%)

simplify87.0ms (2%)

prune220.0ms (5%)

regimes132.0ms (3%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end198.0ms (4.5%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22