Details

sample103.0ms

Algorithm

intervals

Results

35.0ms	44×	body	1280	valid
24.0ms	47×	body	640	valid
15.0ms	137×	body	80	valid
13.0ms	19×	body	320	valid
3.0ms	9×	body	160	valid

simplify327.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	93	16
4	173	16
5	277	16
6	314	16
done	314	16

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite187.0ms

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:

72.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
30.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
82.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series254.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
53.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
115.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.6s

Counts

88 → 88

Iterations

Useful iterations: 2 (268.0ms)

Iter	Nodes	Cost
0	163	1474
1	413	1285
2	2715	1064
done	5001	1064

prune374.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

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

rewrite168.0ms

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:

21.0ms	(/ (sin (* x 0.5)) (sin x))
84.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
55.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (sin (* x 0.5)) (sin x))
127.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
55.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify3.0s

Counts

107 → 107

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	183	1718
1	492	1676
2	3232	1342
done	5000	1292

prune484.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (pow (/ (* 8.0 (sin (* 0.5 x))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

33.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
14.0ms	(/ (sin (* x 0.5)) (sin x))
61.0ms	(* (pow (/ (* 8.0 (sin (* 0.5 x))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
84.0ms	(/ (sin (* x 0.5)) (sin x))
111.0ms	(* (pow (/ (* 8.0 (sin (* 0.5 x))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

simplify1.6s

Counts

109 → 109

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	198	1946
1	493	1729
2	2773	1594
done	5001	1587

prune567.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (pow (* 8.0 (sin (* 0.5 x))) 1) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-exp-log`
85×	`prod-exp`
43×	`add-sqr-sqrt`
41×	`div-exp`
35×	`add-cbrt-cube`
34×	`times-frac`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`associate-l` `pow-exp`
14×	`associate-r`
13×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
9×	`cbrt-undiv` `pow-to-exp`
8×	`pow1`
6×	`unswap-sqr`
5×	`associate-*r/`
4×	`pow-prod-down`
3×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`frac-times` `associate-l/` `-commutative`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `sqr-pow`

Counts

3 → 143

Calls

3 calls:

13.0ms	(/ (sin (* 0.5 x)) (sin x))
42.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
74.0ms	(* (pow (* 8.0 (sin (* 0.5 x))) 1) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

series229.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (sin (* 0.5 x)) (sin x))
76.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
100.0ms	(* (pow (* 8.0 (sin (* 0.5 x))) 1) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

simplify2.7s

Counts

152 → 152

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	234	2916
1	673	2573
2	4198	2033
done	5000	2003

prune408.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	14	20
1	20	18
done	20	18

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	1527×	body	1280	valid
886.0ms	4310×	body	80	valid
820.0ms	1235×	body	640	valid
271.0ms	611×	body	320	valid
74.0ms	317×	body	160	valid