Details

sample82.0ms

Algorithm

intervals

Results

31.0ms	46×	body	1280	valid
20.0ms	49×	body	640	valid
10.0ms	126×	body	80	valid
6.0ms	21×	body	320	valid
3.0ms	14×	body	160	valid

simplify304.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	275
7	275
6	274
5	226
4	134
3	71
2	35
1	20
0	11

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite148.0ms

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:

56.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
25.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
64.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series180.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
83.0ms	(/ (* (* (/ 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	1399
1	411
0	163

prune444.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
31×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`associate-r` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 110

Calls

3 calls:

32.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
15.0ms	(/ (sin x) (sin (* x 0.5)))
24.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
63.0ms	(/ (sin x) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2046
1	549
0	211

prune556.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ 3.0 8.0))
0.2b	(/ (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

1985×	`times-frac`
858×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
108×	`div-inv`
50×	`associate-/l*`
31×	`add-cbrt-cube` `add-exp-log`
29×	`associate-/r*`
19×	`cbrt-undiv` `div-exp`
16×	`associate-/r/`
3×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
1×	`associate-/l/`

Counts

3 → 750

Calls

3 calls:

12.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
39.0ms	(/ (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin x) (sin (* x 0.5))))
9.0ms	(/ (sin x) (sin (* x 0.5)))

series224.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
97.0ms	(/ (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin x) (sin (* x 0.5))))
69.0ms	(/ (sin x) (sin (* x 0.5)))

simplify2.5s

Counts

759 → 759

Iterations

Iter	Nodes
done	5000
1	4647
0	1342

prune5.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
0.3b	(cbrt (* (* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5)))) (/ (sin x) (sin (* x 0.5)))))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
59×	`times-frac`
48×	`*-un-lft-identity` `add-cube-cbrt`
26×	`associate-l`
23×	`add-cbrt-cube` `add-exp-log`
16×	`associate-r`
13×	`pow1` `swap-sqr`
7×	`cbrt-div` `associate-*l/`
6×	`frac-times` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`associate-*r/` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `*-commutative`
1×	`cbrt-prod` `pow2` `clear-num` `frac-2neg` `pow-plus` `pow1/3` `pow3` `pow-sqr` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 143

Calls

4 calls:

9.0ms	(/ (sin x) (sin (* x 0.5)))
52.0ms	(* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
65.0ms	(cbrt (* (* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5)))) (/ (sin x) (sin (* x 0.5)))))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (sin x) (sin (* x 0.5)))
98.0ms	(* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
45.0ms	(cbrt (* (* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5)))) (/ (sin x) (sin (* x 0.5)))))
68.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.2s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
2	2289
1	670
0	235

prune862.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	1532×	body	1280	valid
936.0ms	1246×	body	640	valid
565.0ms	4286×	body	80	valid
289.0ms	607×	body	320	valid
76.0ms	329×	body	160	valid