Details

sample113.0ms

Algorithm

intervals

Results

47.0ms	45×	body	1280	valid
20.0ms	39×	body	640	valid
15.0ms	129×	body	80	valid
10.0ms	27×	body	320	valid
4.0ms	16×	body	160	valid

simplify258.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize27.0ms

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)))
13.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite141.0ms

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×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 79

Calls

3 calls:

55.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
21.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
64.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series198.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
90.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	2720
1	413
0	163

prune426.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

11.0ms	(/ (sin (* x 0.5)) (sin x))
54.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
26.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series215.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (sin (* x 0.5)) (sin x))
119.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.3s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	3184
1	492
0	183

prune539.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 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)))

rewrite60.0ms

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×	`add-log-exp`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 94

Calls

3 calls:

15.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
11.0ms	(/ (sin (* x 0.5)) (sin x))
32.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
64.0ms	(/ (sin (* x 0.5)) (sin x))
114.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify2.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	3331
1	485
0	175

prune511.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac` `add-cbrt-cube` `add-exp-log`
16×	`associate-r`
10×	`pow1`
7×	`prod-exp` `cbrt-unprod`
4×	`associate-l` `pow-prod-down`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l` `add-log-exp`
2×	`associate-r/` `-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*l/`

Counts

3 → 80

Calls

3 calls:

46.0ms	(* (* (sin (* 0.5 x)) (/ (sin (* 0.5 x)) (sin x))) 2.6666666666666665)
14.0ms	(/ (sin (* 0.5 x)) (sin x))
33.0ms	(* (sin (* 0.5 x)) (/ (sin (* 0.5 x)) (sin x)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* (* (sin (* 0.5 x)) (/ (sin (* 0.5 x)) (sin x))) 2.6666666666666665)
43.0ms	(/ (sin (* 0.5 x)) (sin x))
63.0ms	(* (sin (* 0.5 x)) (/ (sin (* 0.5 x)) (sin x)))

simplify2.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	2288
1	344
0	139

prune369.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.7s	1517×	body	1280	valid
664.0ms	1213×	body	640	valid
480.0ms	4311×	body	80	valid
359.0ms	633×	body	320	valid
106.0ms	326×	body	160	valid