Details

sample93.0ms

Algorithm

intervals

Results

26.0ms	45×	body	1280	valid
25.0ms	26×	body	320	valid
16.0ms	42×	body	640	valid
13.0ms	133×	body	80	valid
2.0ms	10×	body	160	valid

simplify502.0ms

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: 16.3b

localize18.0ms

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)))
16.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite131.0ms

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:

51.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
24.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
54.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series168.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
76.0ms	(/ (* (* (/ 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

prune397.0ms

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	(/ (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)))

rewrite91.0ms

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:

10.0ms	(/ (sin (* x 0.5)) (sin x))
50.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
26.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin (* x 0.5)) (sin x))
76.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.7s

Counts

107 → 107

Iterations

Iter	Nodes
done	5002
2	1706
1	490
0	183

prune451.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-cbrt-cube` `add-exp-log`
21×	`times-frac`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r`
12×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
8×	`pow1`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/`
1×	`associate-l` `*-commutative` `associate-/l/`

Counts

3 → 88

Calls

3 calls:

49.0ms	(/ (* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x))) 3.0)
16.0ms	(/ (sin (* x 0.5)) (sin x))
58.0ms	(* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(/ (* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x))) 3.0)
55.0ms	(/ (sin (* x 0.5)) (sin x))
106.0ms	(* (* 8.0 (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5003
2	1796
1	458
0	170

prune449.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 2.6666666666666665 (/ (sin (* 0.5 x)) (sin x)))
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* 2.6666666666666665 (/ (sin (* 0.5 x)) (sin x))) (sin (* 0.5 x)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac` `add-cbrt-cube` `add-exp-log`
16×	`associate-r`
10×	`pow1`
7×	`prod-exp` `cbrt-unprod`
4×	`associate-l` `pow-prod-down`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l` `add-log-exp`
2×	`associate-r/` `-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*l/`

Counts

3 → 80

Calls

3 calls:

14.0ms	(* 2.6666666666666665 (/ (sin (* 0.5 x)) (sin x)))
10.0ms	(/ (sin (* 0.5 x)) (sin x))
48.0ms	(* (* 2.6666666666666665 (/ (sin (* 0.5 x)) (sin x))) (sin (* 0.5 x)))

series233.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(* 2.6666666666666665 (/ (sin (* 0.5 x)) (sin x)))
55.0ms	(/ (sin (* 0.5 x)) (sin x))
92.0ms	(* (* 2.6666666666666665 (/ (sin (* 0.5 x)) (sin x))) (sin (* 0.5 x)))

simplify2.4s

Counts

89 → 89

Iterations

Iter	Nodes
done	5056
3	3900
2	1183
1	340
0	138

prune436.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes85.0ms

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	14
1	14
0	11

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	1467×	body	1280	valid
756.0ms	1247×	body	640	valid
662.0ms	4349×	body	80	valid
606.0ms	626×	body	320	valid
121.0ms	311×	body	160	valid