Details

sample120.0ms

Algorithm

intervals

Results

44.0ms	49×	body	1280	valid
28.0ms	44×	body	640	valid
15.0ms	124×	body	80	valid
11.0ms	26×	body	320	valid
4.0ms	13×	body	160	valid

simplify371.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	313
6	313
5	275
4	171
3	90
2	43
1	20
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize35.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
14×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 85

Calls

3 calls:

73.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
24.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series276.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
71.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
126.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.9s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2504
1	424
0	169

prune576.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

25.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
10.0ms	(/ (sin (* x 0.5)) (sin x))
43.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series216.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
51.0ms	(/ (sin (* x 0.5)) (sin x))
118.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify2.7s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3384
1	499
0	181

prune647.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (sin (* 0.5 x)) (/ (sin x) (sin (* 0.5 x)))) 2.6666666666666665)
0.2b	(/ (sin (* 0.5 x)) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
98×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/l*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 169

Calls

3 calls:

60.0ms	(* (/ (sin (* 0.5 x)) (/ (sin x) (sin (* 0.5 x)))) 2.6666666666666665)
29.0ms	(/ (sin (* 0.5 x)) (/ (sin x) (sin (* 0.5 x))))
14.0ms	(/ (sin x) (sin (* 0.5 x)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(* (/ (sin (* 0.5 x)) (/ (sin x) (sin (* 0.5 x)))) 2.6666666666666665)
103.0ms	(/ (sin (* 0.5 x)) (/ (sin x) (sin (* 0.5 x))))
69.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify2.7s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	4455
1	686
0	255

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (/ (/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0)) (sqrt 3.0)) (/ (sin (* x 0.5)) (sin x)))
0.4b	(/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0))
0.4b	(/ (/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0)) (sqrt 3.0))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
124×	`add-sqr-sqrt`
110×	`sqrt-prod`
105×	`*-un-lft-identity` `add-cube-cbrt`
64×	`associate-l`
52×	`add-cbrt-cube` `add-exp-log`
22×	`cbrt-undiv` `div-exp`
18×	`div-inv`
15×	`associate-/r*`
14×	`associate-/l*`
13×	`associate-r`
12×	`prod-exp` `cbrt-unprod`
6×	`pow1` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 266

Calls

4 calls:

12.0ms	(/ (sin (* x 0.5)) (sin x))
65.0ms	(* (/ (/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0)) (sqrt 3.0)) (/ (sin (* x 0.5)) (sin x)))
16.0ms	(/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0))
31.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0)) (sqrt 3.0))

series828.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (sin (* x 0.5)) (sin x))
398.0ms	(* (/ (/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0)) (sqrt 3.0)) (/ (sin (* x 0.5)) (sin x)))
144.0ms	(/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0))
218.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) (sqrt 3.0)) (sqrt 3.0))

simplify1.2s

Counts

278 → 278

Iterations

Iter	Nodes
done	5001
1	1003
0	339

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes79.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1455×	body	1280	valid
1.3s	4394×	body	80	valid
875.0ms	1234×	body	640	valid
210.0ms	604×	body	320	valid
137.0ms	313×	body	160	valid