Details

sample107.0ms

Algorithm

intervals

Results

48.0ms	313×	body	80	valid
16.0ms	36×	body	640	valid
16.0ms	25×	body	1280	valid
5.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify5.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5009
6	4062
5	1352
4	542
3	196
2	66
1	28
0	12

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* sin (* x cos)) (* sin (* x cos)))
0.6b	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
6.0b	(* sin (* x cos))
6.0b	(* sin (* x cos))

rewrite272.0ms

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:

82.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
130.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
30.0ms	(* sin (* x cos))
24.0ms	(* sin (* x cos))

series257.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
107.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
37.0ms	(* sin (* x cos))
39.0ms	(* sin (* x cos))

simplify1.4s

Counts

158 → 158

Iterations

Iter	Nodes
done	5016
2	1756
1	403
0	147

prune543.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2 x)) (* sin (* x cos)))
0.6b	(/ 1 (* sin (* x cos)))
6.0b	(* sin (* x cos))
6.0b	(* 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-l` `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-r` `-commutative` `div-inv`
1×	`div-sub` `cos-2` `inv-pow`

Counts

4 → 105

Calls

4 calls:

37.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
27.0ms	(/ 1 (* sin (* x cos)))
20.0ms	(* sin (* x cos))
29.0ms	(* sin (* x cos))

series121.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
20.0ms	(/ 1 (* sin (* x cos)))
29.0ms	(* sin (* x cos))
29.0ms	(* sin (* x cos))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5016
2	1096
1	299
0	128

prune559.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize18.0ms

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 cos)))
6.0b	(* sin (* x cos))
6.0b	(* sin (* x cos))

rewrite116.0ms

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:

45.0ms	(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
25.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
27.0ms	(* sin (* x cos))
16.0ms	(* sin (* x cos))

series192.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
39.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
30.0ms	(* sin (* x cos))
30.0ms	(* sin (* x cos))

simplify1.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5186
2	2042
1	442
0	165

prune673.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize51.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* (sin x) (sin x)) (* sin (* x cos)))
6.0b	(* sin (* x cos))
6.0b	(* sin (* x cos))
6.0b	(* sin (* x cos))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
18×	`prod-exp` `cbrt-unprod`
9×	`associate-l` `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-r` `*-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:

42.0ms	(/ (* (sin x) (sin x)) (* sin (* x cos)))
25.0ms	(* sin (* x cos))
16.0ms	(* sin (* x cos))
29.0ms	(* sin (* x cos))

series136.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (* (sin x) (sin x)) (* sin (* x cos)))
32.0ms	(* sin (* x cos))
29.0ms	(* sin (* x cos))
30.0ms	(* sin (* x cos))

simplify1.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	1198
1	260
0	97

prune621.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

regimes258.0ms

Accuracy

0% (0.7b remaining)

Error of 3.1b against oracle of 2.4b and baseline of 3.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	8918×	body	80	valid
1.0s	848×	body	1280	valid
655.0ms	944×	body	640	valid
189.0ms	563×	body	320	valid
72.0ms	300×	body	160	valid