Details

sample109.0ms

Algorithm

intervals

Results

42.0ms	47×	body	1280	valid
22.0ms	40×	body	640	valid
17.0ms	138×	body	80	valid
7.0ms	19×	body	320	valid
4.0ms	12×	body	160	valid

simplify427.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	324
1	20	324
2	43	324
3	90	324
4	171	324
5	275	324
6	313	324
done	313	324

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize39.0ms

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)))
14.3b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite198.0ms

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:

86.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
22.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
87.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series258.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
64.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
130.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.2s

Counts

94 → 94

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	169	31590
1	424	28857
2	2504	28336
done	5000	27616

prune470.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))

rewrite66.0ms

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×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 116

Calls

3 calls:

33.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
9.0ms	(/ (sin x) (sin (* x 0.5)))
21.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
48.0ms	(/ (sin x) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify3.0s

Counts

125 → 125

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	217	47595
1	578	44627
2	3976	44101
done	5000	43661

prune809.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

25.0ms	(* (/ (sin x) (sin (* x 0.5))) 3.0)
13.0ms	(/ (sin x) (sin (* x 0.5)))
35.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* x 0.5))) 3.0))

series213.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* (/ (sin x) (sin (* x 0.5))) 3.0)
49.0ms	(/ (sin x) (sin (* x 0.5)))
88.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* x 0.5))) 3.0))

simplify2.5s

Counts

100 → 100

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	171	37484
1	448	34723
2	2929	34162
done	5002	34042

prune549.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
116×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-r`
31×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
11×	`div-inv`
6×	`prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
5×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 190

Calls

3 calls:

16.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
18.0ms	(/ (sin x) (sin (* x 0.5)))
64.0ms	(* (/ 8.0 3.0) (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))))

series282.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
80.0ms	(/ (sin x) (sin (* x 0.5)))
119.0ms	(* (/ 8.0 3.0) (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))))

simplify1.2s

Counts

199 → 199

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	306	89651
1	943	84768
done	5000	83188

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	324
1	14	324
done	14	324

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.0s	1464×	body	1280	valid
1.0s	1307×	body	640	valid
985.0ms	4289×	body	80	valid
294.0ms	598×	body	320	valid
136.0ms	342×	body	160	valid