Details

sample158.0ms

Algorithm

intervals

Results

57.0ms	274×	body	80	valid
36.0ms	25×	body	640	valid
28.0ms	23×	body	1280	valid
13.0ms	23×	body	320	valid
5.0ms	11×	body	160	valid

simplify550.0ms

Counts

1 → 1

Iterations

Iter	Nodes
7	610
6	610
5	603
4	447
3	163
2	53
1	28
0	12

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

128×	`pow1`
97×	`add-cbrt-cube` `add-exp-log`
72×	`pow-prod-down`
60×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-plus` `associate-l` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `div-sub` `swap-sqr` `cos-2` `div-inv`

Counts

4 → 146

Calls

4 calls:

106.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
102.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
15.0ms	(* (* sin x) cos)
15.0ms	(* (* sin x) cos)

series257.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
71.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
46.0ms	(* (* sin x) cos)
47.0ms	(* (* sin x) cos)

simplify11.3s

Counts

158 → 158

Iterations

Iter	Nodes
3	18002
2	1758
1	402
0	149

prune451.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
0.2b	(/ (cos (* 2 x)) (* (* sin x) cos))
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-cbrt-cube` `add-exp-log`
30×	`prod-exp` `cbrt-unprod`
24×	`cbrt-undiv` `div-exp`
16×	`times-frac`
14×	`pow1`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`associate-/l*`
6×	`associate-r` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`div-sub`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `-commutative` `cos-2`
1×	`associate-/l/`

Counts

4 → 123

Calls

4 calls:

57.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
41.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
23.0ms	(* (* sin x) cos)
15.0ms	(* (* sin x) cos)

series247.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
54.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
33.0ms	(* (* sin x) cos)
35.0ms	(* (* sin x) cos)

simplify575.0ms

Counts

135 → 135

Iterations

Iter	Nodes
2	2265
1	477
0	167

prune587.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* (* (* sin x) cos) (* (* sin x) cos)) (cos (* 2 x))))
0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
129×	`pow1`
114×	`prod-exp`
109×	`add-cbrt-cube`
72×	`pow-prod-down`
60×	`cbrt-unprod`
52×	`div-exp`
33×	`times-frac`
22×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`cbrt-undiv`
11×	`rec-exp` `1-exp`
9×	`pow-sqr` `pow-prod-up`
7×	`associate-/r` `associate-r*`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-plus` `associate-l` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `frac-2neg` `swap-sqr` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 196

Calls

4 calls:

181.0ms	(/ 1 (/ (* (* (* sin x) cos) (* (* sin x) cos)) (cos (* 2 x))))
123.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
29.0ms	(* (* sin x) cos)
36.0ms	(* (* sin x) cos)

series272.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1 (/ (* (* (* sin x) cos) (* (* sin x) cos)) (cos (* 2 x))))
78.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
39.0ms	(* (* sin x) cos)
42.0ms	(* (* sin x) cos)

simplify1.4s

Counts

208 → 208

Iterations

Iter	Nodes
2	3431
1	645
0	237

prune827.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 84

Calls

4 calls:

29.0ms	(* (* sin x) cos)
29.0ms	(* (* sin x) cos)
37.0ms	(* (* sin x) cos)
25.0ms	(* (* sin x) cos)

series148.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* sin x) cos)
30.0ms	(* (* sin x) cos)
37.0ms	(* (* sin x) cos)
52.0ms	(* (* sin x) cos)

simplify2.3s

Counts

96 → 96

Iterations

Iter	Nodes
4	3461
3	1187
2	346
1	106
0	44

prune500.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes324.0ms

Accuracy

0% (2.7b remaining)

Error of 2.8b against oracle of 0.1b and baseline of 2.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.8s	8910×	body	80	valid
1.5s	830×	body	1280	valid
978.0ms	995×	body	640	valid
396.0ms	630×	body	320	valid
151.0ms	295×	body	160	valid