Details

sample110.0ms

Algorithm

intervals

Results

32.0ms	41×	body	1280	valid
22.0ms	35×	body	640	valid
18.0ms	145×	body	80	valid
17.0ms	27×	body	320	valid
3.0ms	8×	body	160	valid

simplify783.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	275
7	275
6	274
5	226
4	134
3	71
2	35
1	20
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize94.0ms

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)))
14.5b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite521.0ms

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:

223.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
75.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
217.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series317.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
61.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
160.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify3.9s

Counts

91 → 91

Iterations

Iter	Nodes
done	5003
2	1336
1	412
0	166

prune951.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize114.0ms

Local error

Found 4 expressions with local error:

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

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
125×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
34×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/r*`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r`
12×	`div-inv`
9×	`associate-/l*`
6×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 215

Calls

4 calls:

27.0ms	(/ 3.0 (sin (* x 0.5)))
141.0ms	(* (/ 8.0 (/ 3.0 (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
57.0ms	(/ (sin (* x 0.5)) (sin x))
58.0ms	(/ 8.0 (/ 3.0 (sin (* x 0.5))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ 3.0 (sin (* x 0.5)))
168.0ms	(* (/ 8.0 (/ 3.0 (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
119.0ms	(/ (sin (* x 0.5)) (sin x))
53.0ms	(/ 8.0 (/ 3.0 (sin (* x 0.5))))

simplify6.5s

Counts

227 → 227

Iterations

Iter	Nodes
done	5000
2	3830
1	956
0	329

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize116.0ms

Local error

Found 4 expressions with local error:

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

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

847×	`times-frac`
444×	`add-sqr-sqrt`
400×	`*-un-lft-identity`
396×	`add-cube-cbrt`
137×	`associate-l`
100×	`add-exp-log`
60×	`associate-/r*`
58×	`div-exp`
52×	`add-cbrt-cube`
37×	`div-inv`
26×	`cbrt-undiv`
16×	`prod-exp`
13×	`associate-r`
12×	`unswap-sqr`
10×	`associate-/r/`
9×	`associate-/l*`
8×	`rec-exp` `1-exp` `cbrt-unprod`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 505

Calls

4 calls:

239.0ms	(* (/ 8.0 (/ 1 (/ (sin (* x 0.5)) 3.0))) (/ (sin (* x 0.5)) (sin x)))
57.0ms	(/ (sin (* x 0.5)) (sin x))
61.0ms	(/ 8.0 (/ 1 (/ (sin (* x 0.5)) 3.0)))
17.0ms	(/ 1 (/ (sin (* x 0.5)) 3.0))

series347.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (/ 8.0 (/ 1 (/ (sin (* x 0.5)) 3.0))) (/ (sin (* x 0.5)) (sin x)))
62.0ms	(/ (sin (* x 0.5)) (sin x))
65.0ms	(/ 8.0 (/ 1 (/ (sin (* x 0.5)) 3.0)))
67.0ms	(/ 1 (/ (sin (* x 0.5)) 3.0))

simplify4.6s

Counts

517 → 517

Iterations

Iter	Nodes
done	5001
1	2301
0	712

prune5.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize118.0ms

Local error

Found 3 expressions with local error:

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

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
31×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`associate-r` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 113

Calls

3 calls:

114.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
27.0ms	(/ (sin x) (sin (* x 0.5)))
51.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series320.0ms

Counts

3 → 9

Calls

3 calls:

154.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
97.0ms	(/ (sin x) (sin (* x 0.5)))
68.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify4.4s

Counts

122 → 122

Iterations

Iter	Nodes
done	5015
2	2003
1	568
0	214

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.6s	1507×	body	1280	valid
1.1s	1337×	body	640	valid
868.0ms	4237×	body	80	valid
311.0ms	601×	body	320	valid
102.0ms	318×	body	160	valid