Details

analyze1.6s (24.5%)

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 (25.7%)

Results

510.0ms	1423×	body	1024	valid
497.0ms	4452×	body	128	valid
438.0ms	1558×	body	512	valid
153.0ms	823×	body	256	valid
1.0ms	1×	body	8192	exit

Compiler

Compiled 33 to 27 computations (18.2% saved)

simplify16.0ms (0.3%)

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

prune3.0ms (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

10.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize10.0ms (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))
✓	2.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series13.0ms (0.2%)

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))

rewrite199.0ms (3.1%)

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:

50.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
22.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify425.0ms (6.6%)

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

prune870.0ms (13.6%)

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

0.1b

Counts

854 → 3

Alt Table

Status	Error	Program
	31.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
▶	24.7b	(/.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)))
✓	10.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 33649 to 26181 computations (22.2% saved)

localize14.0ms (0.2%)

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))
✓	16.0b	(+.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))

rewrite81.0ms (1.3%)

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:

24.0ms	(/.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)))
17.0ms	(+.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))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify178.0ms (2.8%)

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

prune415.0ms (6.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	320	4	324

Error

0.1b

Counts

324 → 4

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	31.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	10.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	24.7b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1)) (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 16749 to 12450 computations (25.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 33

Calls

1 calls:

9.0ms

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

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

736×	`associate-l_binary64`
481×	`distribute-rgt-in_binary64`
462×	`associate-/r*_binary64`
437×	`distribute-lft-in_binary64`
371×	`fma-neg_binary64`

Counts

45 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	975
1	335	727
2	1109	699
3	4461	672
4	4853	671
5	4990	671

prune129.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	151	3	154

Error

0.0b

Counts

154 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	2.9b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))

Compiler

Compiled 3214 to 2414 computations (24.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series10.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

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

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
64×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 152

Calls

3 calls:

15.0ms	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
4.0ms	(/.f64 2 (-.f64 x 1))
2.0ms	(/.f64 1 (fma.f64 x x x))

simplify138.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-neg_binary64`
367×	`fma-def_binary64`
342×	`associate-/l*_binary64`
317×	`associate-*l/_binary64`
297×	`times-frac_binary64`

Counts

188 → 259

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3239
1	549	2947
2	1579	2831
3	4279	2828
4	4762	2828
5	4925	2828

prune202.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	259	3	262

Error

Counts

262 → 3

Alt Table

Status	Error	Program
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(/.f64 (/.f64 2 (+.f64 x -1)) (fma.f64 x x x))
	2.9b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))

Compiler

Compiled 5115 to 3319 computations (35.1% saved)

regimes223.0ms (3.5%)

Accuracy

Total 0.1b remaining (80.9%)

Threshold costs 0.1b (80.9%)

Counts

105 → 1

Compiler

Compiled 3448 to 2622 computations (24% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	15	17
2	16	17
3	14	17

end119.0ms (1.9%)

Compiler: Compiled 65 to 46 computations (29.2% 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

analyze1.6s (24.5%)

sample1.6s (25.7%)

simplify16.0ms (0.3%)

prune3.0ms (0%)

localize10.0ms (0.2%)

series13.0ms (0.2%)

rewrite199.0ms (3.1%)

simplify425.0ms (6.6%)

prune870.0ms (13.6%)

localize14.0ms (0.2%)

series11.0ms (0.2%)

rewrite81.0ms (1.3%)

simplify178.0ms (2.8%)

prune415.0ms (6.5%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify73.0ms (1.1%)

prune129.0ms (2%)

localize10.0ms (0.1%)

series10.0ms (0.2%)

rewrite33.0ms (0.5%)

simplify138.0ms (2.2%)

prune202.0ms (3.2%)

regimes223.0ms (3.5%)

simplify3.0ms (0%)

end119.0ms (1.9%)

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