Details

sample137.0ms

Algorithm

intervals

Results

58.0ms	295×	body	80	valid
24.0ms	32×	body	640	valid
20.0ms	23×	body	1280	valid
8.0ms	19×	body	320	valid
3.0ms	9×	body	160	valid

simplify733.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* sin x) cos) (* (* sin x) cos))
0.6b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
4.5b	(* (* sin x) cos)
4.5b	(* (* sin x) cos)

rewrite244.0ms

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:

102.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
105.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
15.0ms	(* (* sin x) cos)
19.0ms	(* (* sin x) cos)

series226.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
91.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
40.0ms	(* (* sin x) cos)
31.0ms	(* (* sin x) cos)

simplify12.1s

Counts

158 → 158

Iterations

Iter	Nodes
3	17937
2	1878
1	453
0	149

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
0.4b	(/ (cos (* 2 x)) (* (* sin x) cos))
4.5b	(* (* sin x) cos)
4.5b	(* (* sin x) cos)

rewrite127.0ms

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:

53.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
39.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
16.0ms	(* (* sin x) cos)
16.0ms	(* (* sin x) cos)

series216.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
40.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
32.0ms	(* (* sin x) cos)
35.0ms	(* (* sin x) cos)

simplify698.0ms

Counts

135 → 135

Iterations

Iter	Nodes
2	2265
1	477
0	167

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.7b

localize32.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (* sin x) cos)
14.2b	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))
14.2b	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))
14.2b	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `times-frac` `add-cbrt-cube` `add-exp-log`
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` `div-inv`
1×	`associate-l` `*-commutative`

Counts

4 → 78

Calls

4 calls:

31.0ms	(* (* sin x) cos)
22.0ms	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))
30.0ms	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))
22.0ms	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* sin x) cos)
218.0ms	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))
241.0ms	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))
231.0ms	(cbrt (/ (cos (* 2 x)) (* (* sin x) cos)))

simplify1.1s

Counts

90 → 90

Iterations

Iter	Nodes
3	2760
2	758
1	261
0	117

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 1.7b

localize62.0ms

Local error

Found 4 expressions with local error:

14.2b	(cbrt (/ (cos (* 2 x)) (* (* (cbrt (* (* sin x) cos)) (cbrt (* (* sin x) cos))) (cbrt (* (* sin x) cos)))))
14.5b	(cbrt (* (* sin x) cos))
14.5b	(cbrt (* (* sin x) cos))
14.5b	(cbrt (* (* sin x) cos))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac`
1×	`cbrt-div` `div-inv`

Counts

4 → 55

Calls

4 calls:

88.0ms	(cbrt (/ (cos (* 2 x)) (* (* (cbrt (* (* sin x) cos)) (cbrt (* (* sin x) cos))) (cbrt (* (* sin x) cos)))))
21.0ms	(cbrt (* (* sin x) cos))
15.0ms	(cbrt (* (* sin x) cos))
16.0ms	(cbrt (* (* sin x) cos))

series608.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt (/ (cos (* 2 x)) (* (* (cbrt (* (* sin x) cos)) (cbrt (* (* sin x) cos))) (cbrt (* (* sin x) cos)))))
155.0ms	(cbrt (* (* sin x) cos))
138.0ms	(cbrt (* (* sin x) cos))
117.0ms	(cbrt (* (* sin x) cos))

simplify3.4s

Counts

67 → 67

Iterations

Iter	Nodes
4	5602
3	1479
2	507
1	216
0	104

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 1.7b

regimes291.0ms

Accuracy

0% (0.7b remaining)

Error of 3.0b against oracle of 2.3b and baseline of 3.0b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	22
1	22
0	18

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.6s	9027×	body	80	valid
920.0ms	963×	body	640	valid
834.0ms	823×	body	1280	valid
363.0ms	521×	body	320	valid
118.0ms	327×	body	160	valid