Details

sample128.0ms

Algorithm

intervals

Results

68.0ms	57×	body	1280	valid
23.0ms	44×	body	640	valid
14.0ms	123×	body	80	valid
9.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid

simplify329.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	89	16
4	168	16
5	257	16
6	273	16
done	273	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize20.0ms

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)))
12.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
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×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

89.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
88.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series243.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
51.0ms	(* (/ 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

Useful iterations: 2 (276.0ms)

Iter	Nodes	Cost
0	163	1474
1	395	1285
2	1428	1016
done	5000	1016

prune520.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
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` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 98

Calls

3 calls:

19.0ms	(/ (sin (* x 0.5)) (sin x))
89.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series215.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (sin (* x 0.5)) (sin x))
107.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
54.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.7s

Counts

107 → 107

Iterations

Useful iterations: 2 (315.0ms)

Iter	Nodes	Cost
0	183	1718
1	436	1555
2	1584	1292
done	5000	1292

prune364.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 94

Calls

3 calls:

25.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
18.0ms	(/ (sin (* x 0.5)) (sin x))
49.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
45.0ms	(/ (sin (* x 0.5)) (sin x))
103.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	178	1743
1	440	1668
2	1620	1322
done	5001	1318

prune334.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-l`
10×	`times-frac`
9×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
6×	`pow1`
4×	`add-log-exp`
3×	`pow1/3` `associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 65

Calls

4 calls:

31.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))

series426.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
133.0ms	(cbrt (sin x))
142.0ms	(cbrt (sin x))
108.0ms	(cbrt (sin x))

simplify3.8s

Counts

77 → 77

Iterations

Useful iterations: 3 (418.0ms)

Iter	Nodes	Cost
0	113	669
1	247	646
2	615	569
3	1636	560
4	4277	560
done	5000	560

prune276.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	15	16
done	15	16

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1569×	body	1280	valid
1.1s	1216×	body	640	valid
823.0ms	4238×	body	80	valid
263.0ms	643×	body	320	valid
123.0ms	334×	body	160	valid