Details

sample106.0ms

Algorithm

intervals

Results

38.0ms	282×	body	80	valid
26.0ms	28×	body	1280	valid
17.0ms	29×	body	640	valid
7.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid

simplify511.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
0.3b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
3.5b	(* (* sin x) cos)
3.5b	(* (* sin x) cos)

rewrite426.0ms

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×	`insert-posit16` `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 → 138

Calls

4 calls:

75.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
320.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
14.0ms	(* (* sin x) cos)
14.0ms	(* (* sin x) cos)

series244.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
112.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
29.0ms	(* (* sin x) cos)
29.0ms	(* (* sin x) cos)

simplify12.0s

Counts

150 → 150

Iterations

Iter	Nodes
3	16995
2	1803
1	412
0	143

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
0.5b	(/ (cos (* 2 x)) (* (* sin x) cos))
3.5b	(* (* sin x) cos)
3.5b	(* (* sin x) cos)

rewrite135.0ms

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×	`insert-posit16` `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 → 115

Calls

4 calls:

58.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
37.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
15.0ms	(* (* sin x) cos)
23.0ms	(* (* sin x) cos)

series231.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
52.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
49.0ms	(* (* sin x) cos)
38.0ms	(* (* sin x) cos)

simplify727.0ms

Counts

127 → 127

Iterations

Iter	Nodes
2	2275
1	470
0	161

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ 1 (* sin x)) (/ (cos (* 2 x)) cos)) (* (* sin x) cos))
0.5b	(/ 1 (* sin x))
3.3b	(* (/ 1 (* sin x)) (/ (cos (* 2 x)) cos))
3.5b	(* (* sin x) cos)

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

293×	`add-exp-log`
143×	`add-cbrt-cube`
131×	`prod-exp`
109×	`div-exp`
57×	`cbrt-unprod`
51×	`cbrt-undiv`
21×	`add-sqr-sqrt`
18×	`rec-exp` `1-exp`
17×	`times-frac`
16×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
14×	`pow1`
8×	`associate-l`
5×	`pow-prod-down`
4×	`insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
3×	`associate-/l/`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-r/` `-commutative` `pow-flip` `unswap-sqr`
1×	`inv-pow`

Counts

4 → 186

Calls

4 calls:

80.0ms	(/ (* (/ 1 (* sin x)) (/ (cos (* 2 x)) cos)) (* (* sin x) cos))
11.0ms	(/ 1 (* sin x))
36.0ms	(* (/ 1 (* sin x)) (/ (cos (* 2 x)) cos))
39.0ms	(* (* sin x) cos)

series276.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (* (/ 1 (* sin x)) (/ (cos (* 2 x)) cos)) (* (* sin x) cos))
19.0ms	(/ 1 (* sin x))
80.0ms	(* (/ 1 (* sin x)) (/ (cos (* 2 x)) cos))
47.0ms	(* (* sin x) cos)

simplify1.8s

Counts

198 → 198

Iterations

Iter	Nodes
2	4150
1	783
0	261

prune2.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ (/ 1 sin) x) (/ (cos (* 2 x)) cos)) (* (* sin x) cos))
0.3b	(/ (/ 1 sin) x)
3.3b	(* (/ (/ 1 sin) x) (/ (cos (* 2 x)) cos))
3.5b	(* (* sin x) cos)

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

227×	`add-exp-log`
165×	`times-frac`
143×	`add-cbrt-cube`
117×	`add-sqr-sqrt`
107×	`div-exp`
91×	`*-un-lft-identity`
89×	`add-cube-cbrt`
76×	`prod-exp`
60×	`cbrt-undiv`
48×	`cbrt-unprod`
44×	`associate-l`
16×	`associate-r`
14×	`associate-/l*`
11×	`pow1` `div-inv`
9×	`rec-exp` `1-exp`
8×	`unswap-sqr`
4×	`associate-/r*` `pow-prod-down` `insert-posit16` `add-log-exp` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 256

Calls

4 calls:

58.0ms	(/ (* (/ (/ 1 sin) x) (/ (cos (* 2 x)) cos)) (* (* sin x) cos))
15.0ms	(/ (/ 1 sin) x)
44.0ms	(* (/ (/ 1 sin) x) (/ (cos (* 2 x)) cos))
18.0ms	(* (* sin x) cos)

series280.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (* (/ (/ 1 sin) x) (/ (cos (* 2 x)) cos)) (* (* sin x) cos))
11.0ms	(/ (/ 1 sin) x)
81.0ms	(* (/ (/ 1 sin) x) (/ (cos (* 2 x)) cos))
53.0ms	(* (* sin x) cos)

simplify2.1s

Counts

268 → 268

Iterations

Iter	Nodes
2	5655
1	1162
0	380

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes245.0ms

Accuracy

0% (2.5b remaining)

Error of 2.7b against oracle of 0.2b and baseline of 2.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	17
1	17
0	14

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.5s	8922×	body	80	valid
1.0s	816×	body	1280	valid
861.0ms	1002×	body	640	valid
355.0ms	557×	body	320	valid
125.0ms	335×	body	160	valid