Details

sample75.0ms

Algorithm

intervals

Results

26.0ms	45×	body	1280	valid
15.0ms	39×	body	640	valid
10.0ms	129×	body	80	valid
7.0ms	27×	body	320	valid
3.0ms	16×	body	160	valid

simplify323.0ms

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize37.0ms

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))

rewrite159.0ms

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:

69.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
22.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
64.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series226.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
45.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
115.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	2720
1	413
0	163

prune341.0ms

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)))

rewrite136.0ms

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:

17.0ms	(/ (sin (* x 0.5)) (sin x))
77.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (sin (* x 0.5)) (sin x))
79.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.8s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	3184
1	492
0	183

prune418.0ms

Pruning

10 alts after pruning (9 fresh and 1 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	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
36×	`add-sqr-sqrt`
27×	`times-frac`
23×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-cbrt-cube`
13×	`associate-r` `prod-exp`
12×	`div-exp`
11×	`associate-l`
9×	`unpow-prod-down`
6×	`associate-/r*` `pow-exp` `unswap-sqr`
4×	`pow1` `cbrt-undiv` `div-inv` `associate-/l*`
3×	`cbrt-unprod` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 100

Calls

3 calls:

17.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
10.0ms	(/ (sin (* x 0.5)) (sin x))
33.0ms	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

series185.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
46.0ms	(/ (sin (* x 0.5)) (sin x))
94.0ms	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

simplify1.3s

Counts

109 → 109

Iterations

Iter	Nodes
done	5003
2	2617
1	488
0	195

prune648.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
0.3b	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5))))
0.4b	(* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))
1.0b	(/ (cbrt 8.0) (cbrt 3.0))

rewrite569.0ms

Algorithm

rewrite-expression-head

Rules

268×	`add-exp-log`
162×	`add-cbrt-cube`
145×	`prod-exp` `cbrt-unprod`
86×	`times-frac`
82×	`cbrt-prod`
80×	`add-sqr-sqrt`
69×	`cbrt-undiv` `div-exp`
66×	`*-un-lft-identity` `add-cube-cbrt`
46×	`associate-l`
20×	`pow1`
17×	`associate-r`
13×	`associate-*l/`
10×	`pow-prod-down`
6×	`frac-times` `associate-/r` `associate-/l`
5×	`unswap-sqr`
4×	`associate-*r/` `div-inv` `add-log-exp`
3×	`*-commutative`
1×	`clear-num` `frac-2neg`

Counts

4 → 267

Calls

4 calls:

347.0ms	(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
138.0ms	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5))))
53.0ms	(* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))
10.0ms	(/ (cbrt 8.0) (cbrt 3.0))

series773.0ms

Counts

4 → 10

Calls

4 calls:

349.0ms	(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
267.0ms	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5))))
157.0ms	(* (/ (cbrt 8.0) (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ (cbrt 8.0) (cbrt 3.0))

simplify508.0ms

Counts

277 → 277

Iterations

Iter	Nodes
done	5000
1	1197
0	371

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes56.0ms

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	18
1	18
0	13

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	1517×	body	1280	valid
1.2s	1213×	body	640	valid
641.0ms	633×	body	320	valid
547.0ms	4311×	body	80	valid
77.0ms	326×	body	160	valid