Details

sample140.0ms

Algorithm

intervals

Results

59.0ms	270×	body	80	valid
26.0ms	25×	body	1280	valid
22.0ms	31×	body	640	valid
9.0ms	17×	body	320	valid
5.0ms	15×	body	160	valid

simplify986.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	733
7	733
6	732
5	652
4	463
3	164
2	55
1	28
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
4.9b	(* (* sin x) cos)
4.9b	(* (* sin x) cos)

rewrite291.0ms

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:

119.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
135.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
18.0ms	(* (* sin x) cos)
17.0ms	(* (* sin x) cos)

series287.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
100.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
30.0ms	(* (* sin x) cos)
46.0ms	(* (* sin x) cos)

simplify9.8s

Counts

158 → 158

Iterations

Iter	Nodes
3	19256
2	1800
1	410
0	149

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* (* (* sin x) cos) (* (* sin x) cos)) (cos (* 2 x))))
0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
4.9b	(* (* sin x) cos)
4.9b	(* (* sin x) cos)

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
129×	`pow1`
114×	`prod-exp`
109×	`add-cbrt-cube`
72×	`pow-prod-down`
60×	`cbrt-unprod`
52×	`div-exp`
33×	`times-frac`
22×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`cbrt-undiv`
11×	`rec-exp` `1-exp`
9×	`pow-sqr` `pow-prod-up`
7×	`associate-/r` `associate-r*`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-plus` `associate-l` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `frac-2neg` `swap-sqr` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 196

Calls

4 calls:

125.0ms	(/ 1 (/ (* (* (* sin x) cos) (* (* sin x) cos)) (cos (* 2 x))))
103.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
20.0ms	(* (* sin x) cos)
24.0ms	(* (* sin x) cos)

series261.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ 1 (/ (* (* (* sin x) cos) (* (* sin x) cos)) (cos (* 2 x))))
78.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
35.0ms	(* (* sin x) cos)
28.0ms	(* (* sin x) cos)

simplify866.0ms

Counts

208 → 208

Iterations

Iter	Nodes
2	3112
1	653
0	237

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ (* sin (* cos x)) (cos (* x 2))) (* sin (* cos x))))
0.2b	(* (/ (* sin (* cos x)) (cos (* x 2))) (* sin (* cos x)))
4.2b	(* sin (* cos x))
4.2b	(* sin (* cos x))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

246×	`add-exp-log`
138×	`prod-exp`
136×	`add-cbrt-cube`
72×	`cbrt-unprod`
62×	`div-exp`
33×	`pow1`
31×	`cbrt-undiv`
18×	`pow-prod-down`
13×	`rec-exp` `1-exp` `associate-l`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp`
3×	`associate-r` `-commutative` `associate-/l`
2×	`associate-*l/` `div-inv`
1×	`clear-num` `associate-/r*` `frac-2neg` `associate-/r/` `inv-pow`

Counts

4 → 167

Calls

4 calls:

137.0ms	(/ 1 (* (/ (* sin (* cos x)) (cos (* x 2))) (* sin (* cos x))))
70.0ms	(* (/ (* sin (* cos x)) (cos (* x 2))) (* sin (* cos x)))
16.0ms	(* sin (* cos x))
20.0ms	(* sin (* cos x))

series415.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ 1 (* (/ (* sin (* cos x)) (cos (* x 2))) (* sin (* cos x))))
198.0ms	(* (/ (* sin (* cos x)) (cos (* x 2))) (* sin (* cos x)))
38.0ms	(* sin (* cos x))
43.0ms	(* sin (* cos x))

simplify709.0ms

Counts

179 → 179

Iterations

Iter	Nodes
2	2415
1	566
0	208

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
0.3b	(* (* sin (* x cos)) (* sin (* x cos)))
4.2b	(* sin (* x cos))
4.2b	(* sin (* x cos))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
129×	`pow1`
114×	`prod-exp`
109×	`add-cbrt-cube`
72×	`pow-prod-down`
60×	`cbrt-unprod`
52×	`div-exp`
33×	`times-frac`
22×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`cbrt-undiv`
11×	`rec-exp` `1-exp`
9×	`pow-sqr` `pow-prod-up`
7×	`associate-/r` `associate-l*`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-plus` `associate-r` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `frac-2neg` `swap-sqr` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 196

Calls

4 calls:

117.0ms	(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
102.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
27.0ms	(* sin (* x cos))
24.0ms	(* sin (* x cos))

series251.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
68.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
39.0ms	(* sin (* x cos))
45.0ms	(* sin (* x cos))

simplify806.0ms

Counts

208 → 208

Iterations

Iter	Nodes
2	3316
1	637
0	235

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes239.0ms

Accuracy

0% (2.7b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	12

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.4s	9190×	body	80	valid
1.0s	770×	body	1280	valid
845.0ms	930×	body	640	valid
393.0ms	565×	body	320	valid
122.0ms	314×	body	160	valid