Details

sample157.0ms

Algorithm

intervals

Results

54.0ms	295×	body	80	valid
35.0ms	34×	body	1280	valid
19.0ms	25×	body	640	valid
18.0ms	7×	body	160	valid
9.0ms	15×	body	320	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2531
6	2531
5	1352
4	542
3	196
2	66
1	28
0	12

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (* sin cos)) (* x (* sin cos)))
0.3b	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
5.8b	(* x (* sin cos))
5.8b	(* x (* sin cos))

rewrite239.0ms

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-l`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `pow-plus` `associate-r` `-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:

122.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
85.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
13.0ms	(* x (* sin cos))
13.0ms	(* x (* sin cos))

series271.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
103.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
28.0ms	(* x (* sin cos))
33.0ms	(* x (* sin cos))

simplify1.0s

Counts

150 → 150

Iterations

Iter	Nodes
done	2010
2	2010
1	401
0	141

prune367.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
0.6b	(/ (cos (* 2 x)) (* x (* sin cos)))
5.8b	(* x (* sin cos))
5.8b	(* x (* sin cos))

rewrite91.0ms

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-l` `pow-prod-down`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`div-sub`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `cos-2`
1×	`associate-/l/`

Counts

4 → 115

Calls

4 calls:

38.0ms	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
23.0ms	(/ (cos (* 2 x)) (* x (* sin cos)))
13.0ms	(* x (* sin cos))
13.0ms	(* x (* sin cos))

series234.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
54.0ms	(/ (cos (* 2 x)) (* x (* sin cos)))
38.0ms	(* x (* sin cos))
42.0ms	(* x (* sin cos))

simplify892.0ms

Counts

127 → 127

Iterations

Iter	Nodes
done	2003
2	2003
1	431
0	159

prune434.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ 1 x) (/ (cos (* 2 x)) (* sin cos))) (* x (* sin cos)))
0.7b	(/ (cos (* 2 x)) (* sin cos))
5.8b	(* x (* sin cos))
5.8b	(* (/ 1 x) (/ (cos (* 2 x)) (* sin cos)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

251×	`add-exp-log`
143×	`add-cbrt-cube`
107×	`prod-exp`
97×	`div-exp`
57×	`cbrt-unprod`
51×	`cbrt-undiv`
23×	`add-sqr-sqrt`
18×	`times-frac`
17×	`*-un-lft-identity`
16×	`associate-l` `add-cube-cbrt`
12×	`rec-exp` `1-exp`
11×	`pow1`
8×	`associate-r`
4×	`pow-prod-down` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
3×	`unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-r/` `-commutative`
1×	`div-sub` `cos-2`

Counts

4 → 173

Calls

4 calls:

47.0ms	(/ (* (/ 1 x) (/ (cos (* 2 x)) (* sin cos))) (* x (* sin cos)))
21.0ms	(/ (cos (* 2 x)) (* sin cos))
13.0ms	(* x (* sin cos))
25.0ms	(* (/ 1 x) (/ (cos (* 2 x)) (* sin cos)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (* (/ 1 x) (/ (cos (* 2 x)) (* sin cos))) (* x (* sin cos)))
43.0ms	(/ (cos (* 2 x)) (* sin cos))
36.0ms	(* x (* sin cos))
65.0ms	(* (/ 1 x) (/ (cos (* 2 x)) (* sin cos)))

simplify855.0ms

Counts

185 → 185

Iterations

Iter	Nodes
done	2058
2	2058
1	731
0	256

prune731.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ (/ (cos (* 2 x)) sin) cos) x) (* x (* sin cos)))
0.2b	(/ (/ (cos (* 2 x)) sin) cos)
5.8b	(/ (/ (/ (cos (* 2 x)) sin) cos) x)
5.8b	(* x (* sin cos))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

1255×	`times-frac`
529×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
189×	`associate-/l*`
77×	`add-cbrt-cube` `add-exp-log`
49×	`div-inv`
39×	`cbrt-undiv` `div-exp`
15×	`prod-exp` `cbrt-unprod`
9×	`pow1` `div-sub`
7×	`associate-/r*`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `cos-2` `associate-/l/`
1×	`associate-r` `*-commutative`

Counts

4 → 589

Calls

4 calls:

35.0ms	(/ (/ (/ (/ (cos (* 2 x)) sin) cos) x) (* x (* sin cos)))
18.0ms	(/ (/ (cos (* 2 x)) sin) cos)
17.0ms	(/ (/ (/ (cos (* 2 x)) sin) cos) x)
24.0ms	(* x (* sin cos))

series201.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (/ (/ (/ (cos (* 2 x)) sin) cos) x) (* x (* sin cos)))
32.0ms	(/ (/ (cos (* 2 x)) sin) cos)
46.0ms	(/ (/ (/ (cos (* 2 x)) sin) cos) x)
33.0ms	(* x (* sin cos))

simplify957.0ms

Counts

601 → 601

Iterations

Iter	Nodes
done	2000
1	2000
0	927

prune3.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

-6.9% (2.6b remaining)

Error of 2.7b against oracle of 0.1b and baseline of 2.5b

bsearch335.0ms

Steps

Iters	Range		Point
10	1.4434334319750872e-170	5.6768435042774e-159	5.117094630849011e-162
8	-1.2710977012565344e+36	-1.2283864031141439e+33	-2.047820410589973e+33

simplify5.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.1s	9100×	body	80	valid
844.0ms	1014×	body	640	valid
830.0ms	791×	body	1280	valid
652.0ms	561×	body	320	valid
104.0ms	309×	body	160	valid