Details

sample117.0ms

Algorithm

intervals

Results

42.0ms	289×	body	80	valid
23.0ms	40×	body	640	valid
22.0ms	28×	body	1280	valid
11.0ms	9×	body	320	valid
2.0ms	8×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	2319
4	839
3	270
2	75
1	28
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
0.7b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
4.9b	(* (* sin x) cos)
4.9b	(* (* sin x) cos)

rewrite224.0ms

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:

92.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
100.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
14.0ms	(* (* sin x) cos)
14.0ms	(* (* sin x) cos)

series219.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
79.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
33.0ms	(* (* sin x) cos)
38.0ms	(* (* sin x) cos)

simplify1.4s

Counts

158 → 158

Iterations

Iter	Nodes
done	5117
2	2009
1	463
0	149

prune424.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
0.9b	(/ (cos (* 2 x)) (* (* sin x) cos))
4.9b	(* (* sin x) cos)
4.9b	(* (* sin x) cos)

rewrite95.0ms

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:

40.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
22.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
14.0ms	(* (* sin x) cos)
16.0ms	(* (* sin x) cos)

series230.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
56.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
39.0ms	(* (* sin x) cos)
36.0ms	(* (* sin x) cos)

simplify1.6s

Counts

135 → 135

Iterations

Iter	Nodes
done	5040
2	2361
1	478
0	167

prune611.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (* (* sin x) cos))
0.9b	(/ (cos (* 2 x)) (* (* sin x) cos))
4.9b	(* (* sin x) cos)
4.9b	(* (* sin x) cos)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
32×	`add-cbrt-cube`
20×	`pow1`
18×	`prod-exp`
12×	`cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`div-exp` `pow-prod-down`
6×	`cbrt-undiv` `times-frac` `associate-r` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `-commutative` `div-inv`
1×	`div-sub` `cos-2` `inv-pow`

Counts

4 → 105

Calls

4 calls:

26.0ms	(/ 1 (* (* sin x) cos))
24.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
19.0ms	(* (* sin x) cos)
19.0ms	(* (* sin x) cos)

series143.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1 (* (* sin x) cos))
54.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
29.0ms	(* (* sin x) cos)
30.0ms	(* (* sin x) cos)

simplify1.7s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1240
1	323
0	130

prune638.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

4.9b	(* (* sin x) cos)
21.6b	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))
21.6b	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))
21.6b	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-prod`
30×	`times-frac`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-l` `*-commutative`

Counts

4 → 90

Calls

4 calls:

17.0ms	(* (* sin x) cos)
30.0ms	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))
31.0ms	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))
25.0ms	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* sin x) cos)
208.0ms	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))
204.0ms	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))
206.0ms	(cbrt (/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos)))

simplify2.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3960
2	988
1	345
0	149

prune765.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes299.0ms

Accuracy

16.8% (2.2b remaining)

Error of 2.3b against oracle of 0.1b and baseline of 2.8b

bsearch210.0ms

Steps

Iters	Range		Point
6	9.901148865929897e-242	1.351186663093399e-240	3.4016721265247604e-241

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	19

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.9s	8915×	body	80	valid
1.1s	815×	body	1280	valid
951.0ms	987×	body	640	valid
589.0ms	320×	body	160	valid
400.0ms	572×	body	320	valid