Details

analyze1.6s (16.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	99.9%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.6s (17%)

Results

530.0ms	4634×	body	128	valid
477.0ms	1313×	body	1024	valid
425.0ms	1500×	body	512	valid
159.0ms	809×	body	256	valid
1.0ms	2×	body	8192	exit

Compiler

Compiled 50 to 41 computations (18% saved)

simplify16.0ms (0.2%)

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

prune6.0ms (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

9.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize9.0ms (0.1%)

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))
✓	2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series12.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

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

rewrite186.0ms (1.9%)

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:

49.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
21.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify437.0ms (4.6%)

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

prune819.0ms (8.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	851	3	854

Error

0.2b

Counts

854 → 3

Alt Table

Status	Error	Program
	35.9b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
	28.3b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
▶	9.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 2 x) (/.f64 1 (-.f64 x 1))))

Compiler

Compiled 33611 to 26152 computations (22.2% saved)

localize8.0ms (0.1%)

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 2 x) (/.f64 1 (-.f64 x 1)))
✓	2.5b	(-.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 2 x) (/.f64 1 (-.f64 x 1))))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite336.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

1509×	`add-sqr-sqrt_binary64`
1485×	`times-frac_binary64`
1482×	`*-un-lft-identity_binary64`
936×	`prod-diff_binary64`
826×	`add-cube-cbrt_binary64`

Counts

2 → 1090

Calls

2 calls:

71.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 2 x) (/.f64 1 (-.f64 x 1))))
29.0ms	(-.f64 (/.f64 2 x) (/.f64 1 (-.f64 x 1)))

simplify1.3s (13.4%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
370×	`times-frac_binary64`
226×	`+-commutative_binary64`
186×	`fma-udef_binary64`
165×	`fma-def_binary64`

Counts

1114 → 1048

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	526	70194
1	1210	45416
2	3601	44596
3	4588	44596
4	4956	44596

prune1.6s (16.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1177	1	1178
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	1177	4	1181

Error

0.2b

Counts

1181 → 4

Alt Table

Status	Error	Program
	35.9b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
	28.3b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
▶	22.5b	(/.f64 (-.f64 (.f64 1 (.f64 x (-.f64 x 1))) (.f64 (+.f64 x 1) (-.f64 (.f64 2 (-.f64 x 1)) (.f64 x 1)))) (.f64 (+.f64 x 1) (*.f64 x (-.f64 x 1))))
✓	9.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 2 x) (/.f64 1 (-.f64 x 1))))

Compiler

Compiled 63873 to 51325 computations (19.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 x 1))
✓	0.0b	(.f64 (+.f64 x 1) (.f64 x (-.f64 x 1)))
✓	0.2b	(-.f64 (.f64 2 (-.f64 x 1)) (.f64 x 1))
✓	14.5b	(-.f64 (.f64 1 (.f64 x (-.f64 x 1))) (.f64 (+.f64 x 1) (-.f64 (.f64 2 (-.f64 x 1)) (*.f64 x 1))))

series9.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

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

rewrite90.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`distribute-lft-in_binary64`
185×	`distribute-rgt-in_binary64`
148×	`prod-diff_binary64`
130×	`associate--l+_binary64`
125×	`add-sqr-sqrt_binary64`

Counts

4 → 317

Calls

4 calls:

21.0ms	(-.f64 (.f64 1 (.f64 x (-.f64 x 1))) (.f64 (+.f64 x 1) (-.f64 (.f64 2 (-.f64 x 1)) (*.f64 x 1))))
12.0ms	(.f64 (+.f64 x 1) (.f64 x (-.f64 x 1)))
8.0ms	(-.f64 (.f64 2 (-.f64 x 1)) (.f64 x 1))
6.0ms	(*.f64 x (-.f64 x 1))

simplify215.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-neg_binary64`
613×	`associate-l_binary64`
600×	`associate-r_binary64`
512×	`distribute-rgt-in_binary64`
473×	`distribute-lft-in_binary64`

Counts

365 → 497

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	344	7867
1	938	6529
2	4190	5338
3	4824	5333
4	4958	5333

prune833.0ms (8.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	569	1	570
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	570	4	574

Error

0.2b

Counts

574 → 4

Alt Table

Status	Error	Program
	35.9b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
	28.3b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
▶	0.3b	(/.f64 2 (.f64 (+.f64 x 1) (.f64 x (-.f64 x 1))))
✓	9.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (-.f64 (/.f64 2 x) (/.f64 1 (-.f64 x 1))))

Compiler

Compiled 26202 to 19607 computations (25.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 x (-.f64 x 1))
	0.0b	(.f64 (+.f64 x 1) (.f64 x (-.f64 x 1)))
✓	0.3b	(/.f64 2 (.f64 (+.f64 x 1) (.f64 x (-.f64 x 1))))

series4.0ms (0%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(/.f64 2 (*.f64 (+.f64 x 1) (*.f64 x (-.f64 x 1))))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`associate-/r/_binary64`
8×	`associate-*r/_binary64`
4×	`frac-times_binary64`

Counts

1 → 33

Calls

1 calls:

10.0ms

(/.f64 2 (*.f64 (+.f64 x 1) (*.f64 x (-.f64 x 1))))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-r_binary64`
569×	`distribute-rgt-in_binary64`
520×	`distribute-lft-in_binary64`
468×	`associate-/r*_binary64`
289×	`fma-def_binary64`

Counts

45 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	972
1	329	724
2	1155	704
3	4783	704
4	4959	704

prune193.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	238	4	242
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	242	4	246

Error

Counts

246 → 4

Alt Table

Status	Error	Program
	0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(/.f64 (/.f64 2 (+.f64 x 1)) (*.f64 x (-.f64 x 1)))
	0.8b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (+.f64 x 1) (.f64 x (-.f64 x 1))) (sqrt.f64 2)))
	0.6b	(.f64 (/.f64 (sqrt.f64 2) (+.f64 x 1)) (/.f64 (sqrt.f64 2) (.f64 x (-.f64 x 1))))

Compiler

Compiled 5453 to 4046 computations (25.8% saved)

regimes121.0ms (1.3%)

Accuracy

Total 0.1b remaining (84%)

Threshold costs 0.1b (84%)

Counts

41 → 1

Compiler

Compiled 1090 to 836 computations (23.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	16	16
2	17	16
3	15	16

end108.0ms (1.1%)

Compiler: Compiled 76 to 59 computations (22.4% 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

analyze1.6s (16.8%)

sample1.6s (17%)

simplify16.0ms (0.2%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

series12.0ms (0.1%)

rewrite186.0ms (1.9%)

simplify437.0ms (4.6%)

prune819.0ms (8.5%)

localize8.0ms (0.1%)

series7.0ms (0.1%)

rewrite336.0ms (3.5%)

simplify1.3s (13.4%)

prune1.6s (16.2%)

localize13.0ms (0.1%)

series9.0ms (0.1%)

rewrite90.0ms (0.9%)

simplify215.0ms (2.2%)

prune833.0ms (8.7%)

localize6.0ms (0.1%)

series4.0ms (0%)

rewrite12.0ms (0.1%)

simplify58.0ms (0.6%)

prune193.0ms (2%)

regimes121.0ms (1.3%)

simplify2.0ms (0%)

end108.0ms (1.1%)

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