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)

sample53.0ms (1.3%)

Algorithm

1×

intervals

Results

7.0ms	152×	body	128	valid
6.0ms	48×	body	512	valid
5.0ms	31×	body	1024	valid
2.0ms	25×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% 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

prune3.0ms (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

8.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.8b	(+.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))
✓	3.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series18.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(/.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 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))

rewrite195.0ms (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:

47.0ms	(+.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))

simplify424.0ms (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

prune833.0ms (20.2%)

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
✓	8.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	32.8b	(+.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)))))
▶	25.9b	(/.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 33661 to 26191 computations (22.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
✓	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)))
✓	0.0b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	18.5b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series10.0ms (0.3%)

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

rewrite138.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`associate-*l/_binary64`
43×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`

Counts

4 → 188

Calls

4 calls:

80.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
19.0ms	(/.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)))
9.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
4.0ms	(*.f64 (+.f64 x 1) x)

simplify205.0ms (5%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-r_binary64`
441×	`distribute-rgt-in_binary64`
419×	`distribute-lft-in_binary64`
360×	`*-commutative_binary64`
307×	`fma-def_binary64`

Counts

236 → 330

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	5937
1	1057	4948
2	4251	4897
3	4869	4897
4	4988	4897
5	4948	4897

prune507.0ms (12.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	368	2	370
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	370	3	373

Error

0.0b

Counts

373 → 3

Alt Table

Status	Error	Program
✓	8.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	32.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
▶	0.1b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 18434 to 13418 computations (27.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite11.0ms (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:

8.0ms

(/.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

prune161.0ms (3.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	190	5	195

Error

Counts

195 → 5

Alt Table

Status	Error	Program
	21.5b	(*.f64 (sqrt.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x))) (sqrt.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x))))
▶	0.0b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
	0.6b	(/.f64 (sqrt.f64 2) (/.f64 (-.f64 (pow.f64 x 3) x) (sqrt.f64 2)))
	1.7b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))

Compiler

Compiled 3901 to 2868 computations (26.5% saved)

localize53.0ms (1.3%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.2%)

Counts

2 → 15

Calls

2 calls:

4.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
3.0ms	(-.f64 (pow.f64 x 3) x)

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
27×	`times-frac_binary64`

Counts

2 → 125

Calls

2 calls:

6.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
6.0ms	(-.f64 (pow.f64 x 3) x)

simplify136.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-neg_binary64`
649×	`fma-def_binary64`
322×	`associate-/r*_binary64`
268×	`exp-prod_binary64`
264×	`unswap-sqr_binary64`

Counts

140 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2123
1	376	1916
2	1218	1801
3	3802	1801
4	4493	1801
5	4926	1801
6	4870	1801

prune124.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Error

Counts

145 → 5

Alt Table

Status	Error	Program
	21.5b	(*.f64 (sqrt.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x))) (sqrt.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x))))
✓	0.0b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
	0.6b	(/.f64 (sqrt.f64 2) (/.f64 (-.f64 (pow.f64 x 3) x) (sqrt.f64 2)))
	1.7b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))

Compiler

Compiled 2545 to 1545 computations (39.3% saved)

regimes107.0ms (2.6%)

Accuracy

Total 0.2b remaining (96.7%)

Threshold costs 0.2b (96.7%)

Counts

59 → 1

Compiler

Compiled 1750 to 1354 computations (22.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	8	11

end1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample990.0ms (24%)

Algorithm

1×

intervals

Results

226.0ms	4475×	body	128	valid
220.0ms	1250×	body	1024	valid
207.0ms	1511×	body	512	valid
71.0ms	764×	body	256	valid

Compiler

Compiled 97 to 76 computations (21.6% 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%)

sample53.0ms (1.3%)

simplify16.0ms (0.4%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series18.0ms (0.4%)

rewrite195.0ms (4.7%)

simplify424.0ms (10.3%)

prune833.0ms (20.2%)

localize13.0ms (0.3%)

series10.0ms (0.3%)

rewrite138.0ms (3.3%)

simplify205.0ms (5%)

prune507.0ms (12.3%)

localize6.0ms (0.1%)

series5.0ms (0.1%)

rewrite11.0ms (0.3%)

simplify74.0ms (1.8%)

prune161.0ms (3.9%)

localize53.0ms (1.3%)

series6.0ms (0.2%)

rewrite22.0ms (0.5%)

simplify136.0ms (3.3%)

prune124.0ms (3%)

regimes107.0ms (2.6%)

simplify2.0ms (0%)

end1.0ms (0%)

sample990.0ms (24%)

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