Details

sample89.0ms

Algorithm

intervals

Results

62.0ms	190×	body	1280	valid
8.0ms	41×	body	640	valid
7.0ms	224×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify216.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5

prune2.0ms

Filtered

1 candidates to 0 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: 28.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
2.7b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite16.0ms

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` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
11.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
55.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune79.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	1	42

Merged error: 0.0b

Counts

42 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 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`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
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+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series288.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
58.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
47.0ms	(* 1/360 (pow x 6))
40.0ms	(* 1/12 (pow x 4))

simplify54.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423

prune161.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	1	88

Merged error: 0.0b

Counts

88 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.9s	5690×	body	1280	valid
236.0ms	1265×	body	640	valid
236.0ms	8063×	body	80	valid
67.0ms	573×	body	320	valid
23.0ms	306×	body	160	valid