Details

sample64.0ms

Algorithm

intervals

Results

23.0ms	289×	body	80	valid
12.0ms	40×	body	640	valid
12.0ms	28×	body	1280	valid
2.0ms	9×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5009
6	4062
5	1352
4	542
3	196
2	66
1	28
0	12

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize19.0ms

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))))
6.5b	(* sin (* x cos))
6.5b	(* 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-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:

91.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
100.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
18.0ms	(* sin (* x cos))
29.0ms	(* sin (* x cos))

series262.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
108.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
36.0ms	(* sin (* x cos))
30.0ms	(* sin (* x cos))

simplify1.8s

Counts

150 → 150

Iterations

Iter	Nodes
done	5513
2	1743
1	397
0	141

prune476.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.9b

localize25.0ms

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)))
6.5b	(* sin (* x cos))
6.5b	(* sin (* x cos))

rewrite177.0ms

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:

76.0ms	(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
43.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
26.0ms	(* sin (* x cos))
27.0ms	(* sin (* x cos))

series262.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
53.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
50.0ms	(* sin (* x cos))
48.0ms	(* sin (* x cos))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5154
2	2011
1	430
0	159

prune648.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (* 2 x)))
0.9b	(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (/ (* sin (* x cos)) (cbrt (cos (* 2 x)))))
6.5b	(* sin (* x cos))
6.5b	(* sin (* x cos))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
32×	`add-cbrt-cube`
22×	`times-frac`
16×	`prod-exp` `cbrt-unprod`
14×	`pow1` `cbrt-undiv` `div-exp`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`associate-/r*`
9×	`cbrt-prod`
6×	`associate-l` `pow-prod-down`
4×	`insert-posit16` `add-log-exp`
3×	`div-inv`
2×	`associate-r` `*-commutative`
1×	`clear-num` `frac-2neg` `pow1/3` `associate-/r/` `associate-/l*`

Counts

4 → 99

Calls

4 calls:

6.0ms	(cbrt (cos (* 2 x)))
50.0ms	(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (/ (* sin (* x cos)) (cbrt (cos (* 2 x)))))
16.0ms	(* sin (* x cos))
34.0ms	(* sin (* x cos))

series344.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt (cos (* 2 x)))
67.0ms	(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (/ (* sin (* x cos)) (cbrt (cos (* 2 x)))))
48.0ms	(* sin (* x cos))
36.0ms	(* sin (* x cos))

simplify1.6s

Counts

111 → 111

Iterations

Iter	Nodes
done	5022
2	1598
1	439
0	157

prune697.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (* 2 x)))
0.8b	(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
6.5b	(* sin (* x cos))
6.5b	(* sin (* x cos))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-cbrt-cube`
14×	`pow1`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-l` `pow-prod-down` `associate-/l*`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`associate-r` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow1/3` `div-inv`

Counts

4 → 80

Calls

4 calls:

5.0ms	(cbrt (cos (* 2 x)))
28.0ms	(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
30.0ms	(* sin (* x cos))
18.0ms	(* sin (* x cos))

series318.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (cos (* 2 x)))
93.0ms	(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
38.0ms	(* sin (* x cos))
37.0ms	(* sin (* x cos))

simplify2.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5054
3	3818
2	739
1	228
0	104

prune558.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

regimes278.0ms

Accuracy

0% (0.5b remaining)

Error of 2.6b against oracle of 2.2b and baseline of 2.6b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.8s	8915×	body	80	valid
630.0ms	815×	body	1280	valid
557.0ms	987×	body	640	valid
273.0ms	572×	body	320	valid
85.0ms	320×	body	160	valid