Details

sample115.0ms

Algorithm

intervals

Results

39.0ms	299×	body	80	valid
20.0ms	11×	body	160	valid
19.0ms	27×	body	1280	valid
15.0ms	27×	body	640	valid
8.0ms	20×	body	320	valid

simplify899.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	1352
4	542
3	196
2	66
1	28
0	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
0.3b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
4.0b	(* (* sin x) cos)
4.0b	(* (* sin x) cos)

rewrite296.0ms

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:

118.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
130.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
22.0ms	(* (* sin x) cos)
22.0ms	(* (* sin x) cos)

series215.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
76.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
35.0ms	(* (* sin x) cos)
42.0ms	(* (* sin x) cos)

simplify856.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2018
2	1816
1	463
0	149

prune503.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize330.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (* sin x) cos))
0.6b	(/ (cos (* 2 x)) (* (* sin x) cos))
4.0b	(* (* sin x) cos)
4.0b	(* (* sin x) cos)

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
32×	`add-cbrt-cube`
20×	`pow1`
18×	`prod-exp`
12×	`cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`div-exp` `pow-prod-down`
6×	`cbrt-undiv` `times-frac` `associate-r` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `-commutative` `div-inv`
1×	`div-sub` `cos-2` `inv-pow`

Counts

4 → 105

Calls

4 calls:

38.0ms	(/ 1 (* (* sin x) cos))
40.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
22.0ms	(* (* sin x) cos)
15.0ms	(* (* sin x) cos)

series161.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (* (* sin x) cos))
53.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
40.0ms	(* (* sin x) cos)
41.0ms	(* (* sin x) cos)

simplify631.0ms

Counts

117 → 117

Iterations

Iter	Nodes
done	2208
2	1128
1	323
0	130

prune559.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (+ x x)) (* sin (* cos x))) (* sin (* cos x)))
0.6b	(/ (cos (+ x x)) (* sin (* cos x)))
5.6b	(* sin (* cos x))
5.6b	(* sin (* cos x))

rewrite129.0ms

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×	`div-sub` `associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`cos-sum` `clear-num` `associate-/r` `frac-2neg` `count-2` `associate-r` `-commutative` `cos-2`
1×	`associate-/l/`

Counts

4 → 125

Calls

4 calls:

56.0ms	(/ (/ (cos (+ x x)) (* sin (* cos x))) (* sin (* cos x)))
40.0ms	(/ (cos (+ x x)) (* sin (* cos x)))
16.0ms	(* sin (* cos x))
15.0ms	(* sin (* cos x))

series185.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (/ (cos (+ x x)) (* sin (* cos x))) (* sin (* cos x)))
43.0ms	(/ (cos (+ x x)) (* sin (* cos x)))
30.0ms	(* sin (* cos x))
27.0ms	(* sin (* cos x))

simplify828.0ms

Counts

137 → 137

Iterations

Iter	Nodes
done	2000
2	1995
1	435
0	167

prune475.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (+ x x)) sin)
0.2b	(/ (/ (/ (cos (+ x x)) sin) (* cos x)) (* sin (* cos x)))
5.6b	(* sin (* cos x))
5.7b	(/ (/ (cos (+ x x)) sin) (* cos x))

rewrite185.0ms

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`
12×	`div-sub`
9×	`pow1` `div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-sum` `clear-num` `frac-2neg` `count-2` `associate-l` `pow-prod-down` `cos-2`
2×	`associate-/l/`
1×	`associate-r` `*-commutative`

Counts

4 → 185

Calls

4 calls:

35.0ms	(/ (cos (+ x x)) sin)
74.0ms	(/ (/ (/ (cos (+ x x)) sin) (* cos x)) (* sin (* cos x)))
21.0ms	(* sin (* cos x))
52.0ms	(/ (/ (cos (+ x x)) sin) (* cos x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (cos (+ x x)) sin)
81.0ms	(/ (/ (/ (cos (+ x x)) sin) (* cos x)) (* sin (* cos x)))
26.0ms	(* sin (* cos x))
49.0ms	(/ (/ (cos (+ x x)) sin) (* cos x))

simplify514.0ms

Counts

197 → 197

Iterations

Iter	Nodes
done	2001
1	738
0	285

prune730.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	14

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	9042×	body	80	valid
830.0ms	789×	body	1280	valid
771.0ms	971×	body	640	valid
625.0ms	588×	body	320	valid
126.0ms	301×	body	160	valid