Details

sample337.0ms

Algorithm

intervals

Results

16.0ms	440×	body	80	nan
10.0ms	247×	body	80	overflowed
10.0ms	236×	body	80	valid
2.0ms	25×	body	160	valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune25.0ms

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: 5.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.3b	(- (exp x) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
31.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify126.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune306.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	5	136

Merged error: 0.3b

Counts

136 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (exp (* 2.0 x)))
0.5b	(sqrt (exp (* 2.0 x)))
5.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.3b	(- (exp x) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-pow1`
5×	`difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
2.0ms	(sqrt (exp (* 2.0 x)))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series110.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (exp (* 2.0 x)))
22.0ms	(sqrt (exp (* 2.0 x)))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (exp x) 1.0)

simplify108.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5002	361

prune188.0ms

Filtered

74 candidates to 49 candidates (66.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Merged error: 0.2b

Counts

79 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 2.0) (* 1/2 x))
0.5b	(sqrt (exp (* 2.0 x)))
5.3b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
5.3b	(- (exp x) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-log-exp`
7×	`add-cube-cbrt` `difference-of-squares`
6×	`pow1` `sqrt-prod`
5×	`unpow-prod-down`
4×	`add-exp-log` `exp-prod` `pow-pow` `add-cbrt-cube`
3×	`sqrt-pow1` `sqr-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `exp-to-pow` `pow1/2` `pow-exp`

Counts

4 → 66

Calls

4 calls:

3.0ms	(pow (exp 2.0) (* 1/2 x))
2.0ms	(sqrt (exp (* 2.0 x)))
7.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series120.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (exp 2.0) (* 1/2 x))
22.0ms	(sqrt (exp (* 2.0 x)))
56.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	243	428
1	686	409
2	2418	406
3	5002	404

prune237.0ms

Filtered

78 candidates to 54 candidates (69.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	78	4	82

Merged error: 0.0b

Counts

82 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 2.0) (* 1/2 x))
0.1b	(pow (exp 2.0) (* 1/2 x))
5.3b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
5.3b	(- (exp x) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-cube-cbrt` `unpow-prod-down` `pow-pow` `add-log-exp`
7×	`difference-of-squares`
6×	`pow1` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
3×	`sqrt-prod`
2×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--`

Counts

4 → 69

Calls

4 calls:

3.0ms	(pow (exp 2.0) (* 1/2 x))
3.0ms	(pow (exp 2.0) (* 1/2 x))
7.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series129.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (exp 2.0) (* 1/2 x))
27.0ms	(pow (exp 2.0) (* 1/2 x))
52.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	445
1	636	429
2	2236	426
3	5001	426

prune216.0ms

Filtered

81 candidates to 58 candidates (71.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	81	4	85

Merged error: 0.0b

Counts

85 → 4

Details

sample337.0ms

simplify76.0ms

prune25.0ms

localize12.0ms

rewrite35.0ms

series202.0ms

simplify126.0ms

prune306.0ms

localize13.0ms

rewrite16.0ms

series110.0ms

simplify108.0ms

prune188.0ms

localize20.0ms

rewrite18.0ms

series120.0ms

simplify71.0ms

prune237.0ms

localize16.0ms

rewrite19.0ms

series129.0ms

simplify65.0ms

prune216.0ms

regimes33.0ms

bsearch4.0ms

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