Details

sample118.0ms

Algorithm

intervals

Results

47.0ms	297×	body	80	valid
24.0ms	28×	body	1280	valid
17.0ms	23×	body	640	valid
9.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid

simplify620.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.2b

localize19.0ms

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)))
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)

rewrite236.0ms

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:

82.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
98.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
26.0ms	(* (* sin x) cos)
26.0ms	(* (* sin x) cos)

series251.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
98.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
48.0ms	(* (* sin x) cos)
34.0ms	(* (* sin x) cos)

simplify11.0s

Counts

158 → 158

Iterations

Iter	Nodes
3	17937
2	1878
1	453
0	149

prune802.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
0.3b	(/ (cos (* 2 x)) (* (* sin x) cos))
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)

rewrite159.0ms

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:

47.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
46.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
31.0ms	(* (* sin x) cos)
35.0ms	(* (* sin x) cos)

series239.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
66.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
34.0ms	(* (* sin x) cos)
33.0ms	(* (* sin x) cos)

simplify709.0ms

Counts

135 → 135

Iterations

Iter	Nodes
2	2265
1	477
0	167

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.4b

localize63.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* (sin x) (sin x)) (* (* sin x) cos))
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
18×	`prod-exp` `cbrt-unprod`
9×	`associate-r` `pow-prod-down`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `div-sub` `sqr-sin` `div-inv` `sin-mult` `associate-/l` `associate-/l/`

Counts

4 → 93

Calls

4 calls:

46.0ms	(/ (* (sin x) (sin x)) (* (* sin x) cos))
35.0ms	(* (* sin x) cos)
30.0ms	(* (* sin x) cos)
30.0ms	(* (* sin x) cos)

series149.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* (sin x) (sin x)) (* (* sin x) cos))
33.0ms	(* (* sin x) cos)
37.0ms	(* (* sin x) cos)
28.0ms	(* (* sin x) cos)

simplify5.1s

Counts

105 → 105

Iterations

Iter	Nodes
3	11275
2	1410
1	279
0	99

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
0.6b	(/ (cos (* 2 x)) (* sin x))
5.5b	(/ (/ (cos (* 2 x)) (* sin x)) cos)
5.6b	(* (* sin x) cos)

rewrite141.0ms

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:

43.0ms	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
22.0ms	(/ (cos (* 2 x)) (* sin x))
35.0ms	(/ (/ (cos (* 2 x)) (* sin x)) cos)
35.0ms	(* (* sin x) cos)

series251.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
55.0ms	(/ (cos (* 2 x)) (* sin x))
68.0ms	(/ (/ (cos (* 2 x)) (* sin x)) cos)
29.0ms	(* (* sin x) cos)

simplify1.3s

Counts

200 → 200

Iterations

Iter	Nodes
2	3297
1	843
0	304

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

0% (2.7b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	15
1	15
0	13

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.0s	9122×	body	80	valid
1.5s	937×	body	640	valid
967.0ms	872×	body	1280	valid
436.0ms	587×	body	320	valid
120.0ms	302×	body	160	valid