Details

sample82.0ms

Algorithm

intervals

Results

31.0ms	44×	body	1280	valid
15.0ms	29×	body	640	valid
15.0ms	148×	body	80	valid
8.0ms	24×	body	320	valid
2.0ms	11×	body	160	valid

simplify303.0ms

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: 15.3b

localize27.0ms

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)))
15.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite168.0ms

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*` `insert-posit16` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 82

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
25.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
82.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series195.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
82.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.7s

Counts

91 → 91

Iterations

Iter	Nodes
done	5003
2	1441
1	414
0	166

prune317.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
98×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/l*`
5×	`pow1`
3×	`associate-r` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 166

Calls

3 calls:

33.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
29.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
11.0ms	(/ (sin x) (sin (* x 0.5)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
69.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
44.0ms	(/ (sin x) (sin (* x 0.5)))

simplify1.7s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	2441
1	677
0	255

prune659.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))
0.3b	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
111×	`add-sqr-sqrt`
93×	`*-un-lft-identity` `add-cube-cbrt`
45×	`associate-l`
34×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
12×	`associate-r`
11×	`pow1`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
9×	`sqrt-prod`
6×	`associate-/l*` `unswap-sqr`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`associate-*l/`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`

Counts

4 → 199

Calls

4 calls:

26.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
11.0ms	(/ (sin x) (sin (* x 0.5)))
31.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))
53.0ms	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))

series387.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
55.0ms	(/ (sin x) (sin (* x 0.5)))
122.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))
152.0ms	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))

simplify2.0s

Counts

211 → 211

Iterations

Iter	Nodes
done	5002
2	3013
1	807
0	297

prune881.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (sin x))
0.1b	(* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5)))
0.3b	(* (* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5))) (sqrt 2.6666666666666665))
0.3b	(* (* (* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`pow1`
19×	`times-frac`
16×	`prod-exp` `cbrt-unprod`
15×	`associate-r` `associate-l`
10×	`pow-prod-down`
6×	`associate-*l/` `sqrt-prod`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*`
2×	`div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg`

Counts

4 → 114

Calls

4 calls:

12.0ms	(/ (sin (* x 0.5)) (sin x))
25.0ms	(* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5)))
71.0ms	(* (* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5))) (sqrt 2.6666666666666665))
141.0ms	(* (* (* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))

series406.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (sin (* x 0.5)) (sin x))
85.0ms	(* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5)))
125.0ms	(* (* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5))) (sqrt 2.6666666666666665))
150.0ms	(* (* (* (/ (sin (* x 0.5)) (sin x)) (sin (* x 0.5))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))

simplify1.7s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1624
1	482
0	187

prune412.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes129.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.7s	1494×	body	1280	valid
1.1s	1210×	body	640	valid
597.0ms	4328×	body	80	valid
264.0ms	625×	body	320	valid
86.0ms	343×	body	160	valid