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)

sample58.0ms (1.4%)

Algorithm

1×

intervals

Results

12.0ms	42×	body	1024	valid
8.0ms	58×	body	512	valid
7.0ms	139×	body	128	valid
2.0ms	17×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify19.0ms (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 (0.1%)

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

10.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.5b	(+.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))
✓	2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series11.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(+.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))

rewrite188.0ms (4.7%)

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)))
18.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify418.0ms (10.4%)

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

prune855.0ms (21.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	850	4	854

Error

0.3b

Counts

854 → 4

Alt Table

Status	Error	Program
▶	26.5b	(/.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)))
	32.3b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
	31.8b	(fma.f64 -2 x (/.f64 -2 x))
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 33651 to 26181 computations (22.2% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	0.0b	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	16.3b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series8.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
2.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
1.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
1.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite52.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
55×	`prod-diff_binary64`
55×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
46×	`associate-*l/_binary64`

Counts

4 → 188

Calls

4 calls:

11.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
11.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
9.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify149.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
626×	`associate-l_binary64`
459×	`associate-r_binary64`
377×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`

Counts

236 → 303

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5247
1	827	4042
2	3405	3411
3	4686	3405
4	5206	3405

prune348.0ms (8.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	304	3	307

Error

0.3b

Counts

307 → 3

Alt Table

Status	Error	Program
	32.3b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
▶	0.3b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 14313 to 10642 computations (25.6% 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))
✓	0.3b	(/.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)))

rewrite13.0ms (0.3%)

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:

10.0ms

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

simplify74.0ms (1.8%)

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

prune131.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
	21.0b	(.f64 (/.f64 2 (.f64 (-.f64 x 1) (+.f64 x (pow.f64 x 4)))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1))))
	0.6b	(*.f64 (/.f64 (sqrt.f64 2) (fma.f64 x x x)) (/.f64 (sqrt.f64 2) (-.f64 x 1)))
	0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
✓	0.3b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
▶	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))

Compiler

Compiled 3263 to 2431 computations (25.5% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
✓	0.4b	(/.f64 2 (fma.f64 x x x))

series7.0ms (0.2%)

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 (0.7%)

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))
2.0ms	(/.f64 2 (fma.f64 x x x))

simplify185.0ms (4.6%)

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

prune144.0ms (3.6%)

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
	21.0b	(.f64 (/.f64 2 (.f64 (-.f64 x 1) (+.f64 x (pow.f64 x 4)))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1))))
	0.8b	(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (-.f64 (pow.f64 x 3) x)))
	0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
✓	0.3b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))

Compiler

Compiled 4700 to 2757 computations (41.3% saved)

regimes109.0ms (2.7%)

Accuracy

Total 0.1b remaining (86.8%)

Threshold costs 0.1b (86.8%)

Counts

50 → 1

Compiler

Compiled 1520 to 1130 computations (25.7% saved)

simplify2.0ms (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

end0.0ms (0%)

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

sample1.2s (29.4%)

Algorithm

1×

intervals

Results

326.0ms	1293×	body	1024	valid
233.0ms	1547×	body	512	valid
228.0ms	4409×	body	128	valid
145.0ms	751×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 96 to 72 computations (25% 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%)

sample58.0ms (1.4%)

simplify19.0ms (0.5%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series11.0ms (0.3%)

rewrite188.0ms (4.7%)

simplify418.0ms (10.4%)

prune855.0ms (21.2%)

localize14.0ms (0.4%)

series8.0ms (0.2%)

rewrite52.0ms (1.3%)

simplify149.0ms (3.7%)

prune348.0ms (8.6%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite13.0ms (0.3%)

simplify74.0ms (1.8%)

prune131.0ms (3.2%)

localize9.0ms (0.2%)

series7.0ms (0.2%)

rewrite28.0ms (0.7%)

simplify185.0ms (4.6%)

prune144.0ms (3.6%)

regimes109.0ms (2.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (29.4%)

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