Details

sample64.0ms

Algorithm

intervals

Results

26.0ms	55×	body	2560	valid
18.0ms	49×	body	1280	valid
5.0ms	34×	body	640	valid
3.0ms	30×	body	320	valid
3.0ms	71×	body	80	valid
1.0ms	17×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

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: 32.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.3b	(- 1.0 (cos x))
17.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify61.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune107.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	39	9	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	9	49

Merged error: 0.1b

Counts

49 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
13.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 1/720 (pow x 4))
5.0ms	(* 1/24 (pow x 2))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series107.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 1/720 (pow x 4))
28.0ms	(* 1/24 (pow x 2))
43.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	268	345
1	1132	313
2	5001	307

prune138.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 0.1b

Counts

84 → 9

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.3b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

9.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series111.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
43.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune249.0ms

Filtered

156 candidates to 104 candidates (66.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	151	5	156
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	155	10	165

Merged error: 0.1b

Counts

165 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
2.4b	(- (/ 1.0 x) (/ (cos x) x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
95×	`times-frac`
78×	`*-un-lft-identity`
38×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/l*`
12×	`div-inv`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 118

Calls

3 calls:

16.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms	(/ (cos x) x)
15.0ms	(- (/ 1.0 x) (/ (cos x) x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
30.0ms	(/ (cos x) x)
60.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify46.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	463	1015
1	1518	940
2	5002	936

prune222.0ms

Filtered

127 candidates to 99 candidates (78.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	128	9	137

Merged error: 0.1b

Counts

137 → 9

Details

sample64.0ms

simplify7.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series65.0ms

simplify61.0ms

prune107.0ms

localize12.0ms

rewrite19.0ms

series107.0ms

simplify41.0ms

prune138.0ms

localize6.0ms

rewrite25.0ms

series111.0ms

simplify53.0ms

prune249.0ms

localize7.0ms

rewrite41.0ms

series188.0ms

simplify46.0ms

prune222.0ms

regimes74.0ms

bsearch2.0ms

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