Details

analyze66.0ms (1.3%)

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)

sample44.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	45×	body	1024	valid
8.0ms	152×	body	128	valid
5.0ms	39×	body	512	valid
2.0ms	20×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify26.0ms (0.5%)

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

prune2.0ms (0%)

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

10.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.2b	(+.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 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	2.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series54.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
3.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))

rewrite200.0ms (4%)

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:

48.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(/.f64 1 (-.f64 x 1))

simplify513.0ms (10.2%)

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

prune964.0ms (19.2%)

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

0.2b

Counts

854 → 3

Alt Table

Status	Error	Program
	33.0b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
✓	10.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	25.7b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 33637 to 26171 computations (22.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.2b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	16.1b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series11.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
3.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
2.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
2.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite74.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`associate-*l/_binary64`
39×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
37×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`

Counts

4 → 181

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
12.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
10.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
4.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify245.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-r_binary64`
442×	`distribute-rgt-in_binary64`
409×	`distribute-lft-in_binary64`
342×	`*-commutative_binary64`
307×	`fma-def_binary64`

Counts

229 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	6310
1	1064	4993
2	4286	4902
3	4952	4894
4	4946	4894

prune447.0ms (8.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	320	1	321
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	320	4	324

Error

0.2b

Counts

324 → 4

Alt Table

Status	Error	Program
	33.0b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
✓	10.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	0.3b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	25.7b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 16713 to 12422 computations (25.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
2.0ms	(*.f64 (+.f64 x 1) x)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`associate-*l/_binary64`
8×	`associate-/r/_binary64`
8×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

7.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
4.0ms	(*.f64 (+.f64 x 1) x)

simplify98.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-/r*_binary64`
506×	`distribute-rgt-in_binary64`
466×	`distribute-lft-in_binary64`
324×	`fma-def_binary64`
187×	`times-frac_binary64`

Counts

80 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1295
1	365	957
2	1226	936
3	4668	936
4	4964	936
5	4951	936

prune203.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	188	5	193

Error

Counts

193 → 5

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
✓	10.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	0.6b	(.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 x (fma.f64 x x -1)))) (cbrt.f64 (/.f64 2 (.f64 x (fma.f64 x x -1))))) (cbrt.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1)))))
	0.2b	(/.f64 2 (.f64 (+.f64 x 1) (-.f64 (.f64 x x) x)))
	0.2b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 3895 to 2859 computations (26.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
✓	0.2b	(/.f64 2 (fma.f64 x x x))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
3.0ms	(/.f64 2 (fma.f64 x x x))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`times-frac_binary64`
136×	`add-sqr-sqrt_binary64`
122×	`*-un-lft-identity_binary64`
80×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`

Counts

2 → 159

Calls

2 calls:

7.0ms	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
3.0ms	(/.f64 2 (fma.f64 x x x))

simplify227.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-neg_binary64`
414×	`associate-/r*_binary64`
384×	`associate-/l/_binary64`
300×	`fma-def_binary64`
235×	`times-frac_binary64`

Counts

183 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	4872
1	618	4739
2	1619	4586
3	4340	4553
4	4701	4553
5	4955	4553

prune215.0ms (4.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	222	5	227

Error

Counts

227 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
✓	10.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	0.2b	(/.f64 2 (.f64 (+.f64 x 1) (-.f64 (.f64 x x) x)))
	0.2b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.6b	(.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x))) (cbrt.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x)))) (cbrt.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x))))

Compiler

Compiled 4707 to 2762 computations (41.3% saved)

regimes480.0ms (9.6%)

Accuracy

Total 0.1b remaining (82.9%)

Threshold costs 0.1b (82.9%)

Counts

204 → 1

Compiler

Compiled 8280 to 6112 computations (26.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	13	14
2	14	14
3	12	14

end1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample1.0s (20.9%)

Algorithm

1×

intervals

Results

266.0ms	1370×	body	1024	valid
225.0ms	4422×	body	128	valid
212.0ms	1436×	body	512	valid
77.0ms	772×	body	256	valid

Compiler

Compiled 103 to 77 computations (25.2% 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

analyze66.0ms (1.3%)

sample44.0ms (0.9%)

simplify26.0ms (0.5%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series54.0ms (1.1%)

rewrite200.0ms (4%)

simplify513.0ms (10.2%)

prune964.0ms (19.2%)

localize15.0ms (0.3%)

series11.0ms (0.2%)

rewrite74.0ms (1.5%)

simplify245.0ms (4.9%)

prune447.0ms (8.9%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite15.0ms (0.3%)

simplify98.0ms (1.9%)

prune203.0ms (4%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite28.0ms (0.6%)

simplify227.0ms (4.5%)

prune215.0ms (4.3%)

regimes480.0ms (9.6%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.0s (20.9%)

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