Details

sample130.0ms

Algorithm

intervals

Results

55.0ms	291×	body	80	valid
21.0ms	28×	body	640	valid
18.0ms	17×	body	1280	valid
15.0ms	25×	body	320	valid
3.0ms	9×	body	160	valid

simplify586.0ms

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
0.5b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
5.5b	(* (* sin x) cos)
5.5b	(* (* sin x) cos)

rewrite259.0ms

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:

108.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
110.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
23.0ms	(* (* sin x) cos)
14.0ms	(* (* sin x) cos)

series256.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
95.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
36.0ms	(* (* sin x) cos)
41.0ms	(* (* sin x) cos)

simplify10.6s

Counts

158 → 158

Iterations

Iter	Nodes
3	17937
2	1878
1	453
0	149

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.2b

localize37.0ms

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))
5.5b	(* (* sin x) cos)
5.5b	(* (* sin x) cos)

rewrite170.0ms

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:

85.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
46.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
15.0ms	(* (* sin x) cos)
22.0ms	(* (* sin x) cos)

series259.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
75.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
38.0ms	(* (* sin x) cos)
42.0ms	(* (* sin x) cos)

simplify751.0ms

Counts

135 → 135

Iterations

Iter	Nodes
2	2265
1	477
0	167

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt cos) (cbrt cos))
1.4b	(* (* (* sin x) (* (cbrt cos) (cbrt cos))) (cbrt cos))
4.3b	(* (* sin x) (* (cbrt cos) (cbrt cos)))
5.5b	(* (* sin x) cos)

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
41×	`add-exp-log`
26×	`add-cbrt-cube` `pow-prod-down`
25×	`prod-exp` `cbrt-unprod`
23×	`add-sqr-sqrt`
19×	`cbrt-prod`
16×	`associate-r`
15×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
6×	`pow1/3` `swap-sqr`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 122

Calls

4 calls:

8.0ms	(* (cbrt cos) (cbrt cos))
100.0ms	(* (* (* sin x) (* (cbrt cos) (cbrt cos))) (cbrt cos))
28.0ms	(* (* sin x) (* (cbrt cos) (cbrt cos)))
26.0ms	(* (* sin x) cos)

series598.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(* (cbrt cos) (cbrt cos))
73.0ms	(* (* (* sin x) (* (cbrt cos) (cbrt cos))) (cbrt cos))
159.0ms	(* (* sin x) (* (cbrt cos) (cbrt cos)))
43.0ms	(* (* sin x) cos)

simplify2.8s

Counts

134 → 134

Iterations

Iter	Nodes
3	4958
2	1309
1	375
0	147

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
0.8b	(/ (cos (* 2 x)) (* sin x))
5.5b	(* (* sin x) cos)
5.7b	(/ (/ (cos (* 2 x)) (* sin x)) cos)

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

121×	`times-frac`
77×	`add-cbrt-cube` `add-exp-log`
51×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
35×	`associate-/l*`
34×	`cbrt-undiv` `div-exp`
20×	`prod-exp` `cbrt-unprod`
15×	`div-inv`
9×	`pow1`
6×	`div-sub`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-prod-down` `cos-2`
2×	`associate-/l/`
1×	`associate-l` `*-commutative`

Counts

4 → 188

Calls

4 calls:

47.0ms	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
36.0ms	(/ (cos (* 2 x)) (* sin x))
30.0ms	(* (* sin x) cos)
36.0ms	(/ (/ (cos (* 2 x)) (* sin x)) cos)

series275.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
67.0ms	(/ (cos (* 2 x)) (* sin x))
48.0ms	(* (* sin x) cos)
56.0ms	(/ (/ (cos (* 2 x)) (* sin x)) cos)

simplify1.1s

Counts

200 → 200

Iterations

Iter	Nodes
2	3280
1	840
0	304

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes265.0ms

Accuracy

0% (2.8b remaining)

Error of 2.9b against oracle of 0.1b and baseline of 2.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	8980×	body	80	valid
1.4s	1024×	body	640	valid
1.0s	835×	body	1280	valid
420.0ms	579×	body	320	valid
123.0ms	313×	body	160	valid