Details

sample88.0ms

Algorithm

intervals

Results

38.0ms	309×	body	80	valid
14.0ms	21×	body	1280	valid
13.0ms	27×	body	640	valid
6.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2531
6	2531
5	1352
4	542
3	196
2	66
1	28
0	12

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (* sin cos)) (* x (* sin cos)))
0.3b	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
6.8b	(* x (* sin cos))
6.8b	(* x (* sin cos))

rewrite245.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 146

Calls

4 calls:

95.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
106.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
16.0ms	(* x (* sin cos))
23.0ms	(* x (* sin cos))

series217.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
81.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
31.0ms	(* x (* sin cos))
41.0ms	(* x (* sin cos))

simplify1.2s

Counts

158 → 158

Iterations

Iter	Nodes
done	2000
3	2000
2	1897
1	403
0	147

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
0.9b	(/ (cos (* 2 x)) (* x (* sin cos)))
6.8b	(* x (* sin cos))
6.8b	(* x (* sin cos))

rewrite150.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 123

Calls

4 calls:

59.0ms	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
28.0ms	(/ (cos (* 2 x)) (* x (* sin cos)))
27.0ms	(* x (* sin cos))
32.0ms	(* x (* sin cos))

series268.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
57.0ms	(/ (cos (* 2 x)) (* x (* sin cos)))
36.0ms	(* x (* sin cos))
45.0ms	(* x (* sin cos))

simplify952.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	2000
2	2000
1	441
0	165

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2 x)) x)
0.2b	(/ (/ (/ (cos (* 2 x)) x) (* sin cos)) (* x (* sin cos)))
6.8b	(* x (* sin cos))
7.0b	(/ (/ (cos (* 2 x)) x) (* sin cos))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

101×	`times-frac`
92×	`add-cbrt-cube` `add-exp-log`
43×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
40×	`cbrt-undiv` `div-exp`
33×	`associate-/l*`
26×	`prod-exp` `cbrt-unprod`
9×	`pow1` `div-inv`
6×	`div-sub`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `cos-2`
2×	`associate-/l/`
1×	`associate-r` `*-commutative`

Counts

4 → 182

Calls

4 calls:

12.0ms	(/ (cos (* 2 x)) x)
36.0ms	(/ (/ (/ (cos (* 2 x)) x) (* sin cos)) (* x (* sin cos)))
27.0ms	(* x (* sin cos))
31.0ms	(/ (/ (cos (* 2 x)) x) (* sin cos))

series208.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (cos (* 2 x)) x)
79.0ms	(/ (/ (/ (cos (* 2 x)) x) (* sin cos)) (* x (* sin cos)))
40.0ms	(* x (* sin cos))
47.0ms	(/ (/ (cos (* 2 x)) x) (* sin cos))

simplify1.2s

Counts

194 → 194

Iterations

Iter	Nodes
done	2001
2	2001
1	735
0	279

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* sin (* cos x)) (* sin (* cos x)))
0.3b	(/ (cos (* 2 x)) (* (* sin (* cos x)) (* sin (* cos x))))
3.4b	(* sin (* cos x))
3.4b	(* sin (* cos x))

rewrite271.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 146

Calls

4 calls:

116.0ms	(* (* sin (* cos x)) (* sin (* cos x)))
104.0ms	(/ (cos (* 2 x)) (* (* sin (* cos x)) (* sin (* cos x))))
14.0ms	(* sin (* cos x))
31.0ms	(* sin (* cos x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (* sin (* cos x)) (* sin (* cos x)))
131.0ms	(/ (cos (* 2 x)) (* (* sin (* cos x)) (* sin (* cos x))))
39.0ms	(* sin (* cos x))
36.0ms	(* sin (* cos x))

simplify1.4s

Counts

158 → 158

Iterations

Iter	Nodes
done	2002
3	2002
2	1889
1	403
0	147

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

19% (2.5b remaining)

Error of 2.6b against oracle of 0.1b and baseline of 3.2b

bsearch317.0ms

Steps

Iters	Range		Point
8	2.16529498834443e+179	2.789034697247755e+182	2.3583945307121096e+180
9	4.700193106470597e-272	1.496691526338484e-266	1.2328361595450645e-266

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	26

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.5s	9077×	body	80	valid
1.2s	798×	body	1280	valid
819.0ms	950×	body	640	valid
391.0ms	596×	body	320	valid
161.0ms	282×	body	160	valid