Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample74.0ms

Algorithm

intervals

Results

58.0ms	188×	body	1280	valid
6.0ms	35×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5718	8

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.6b

Counts

2 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.9b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `associate-+l+` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 33

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
8.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5310	423

prune54.0ms

Filtered

27 candidates to 39 candidates (-44.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	40	1	41

Merged error: 0b

Counts

41 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+`

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series28.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
12.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
6.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5022	849

prune121.0ms

Filtered

56 candidates to 86 candidates (-53.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	1	87

Merged error: 0b

Counts

87 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.7s	5569×	body	1280	valid
223.0ms	1281×	body	640	valid
69.0ms	636×	body	320	valid
24.0ms	348×	body	160	valid
6.0ms	166×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample74.0ms

simplify40.0ms

prune12.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify53.0ms

prune54.0ms

localize9.0ms

rewrite24.0ms

series28.0ms

simplify52.0ms

prune121.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling