Details

sample114.0ms

Algorithm

intervals

Results

51.0ms	53×	body	1280	valid
24.0ms	45×	body	640	valid
16.0ms	131×	body	80	valid
4.0ms	12×	body	320	valid
4.0ms	15×	body	160	valid

simplify313.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	313
6	313
5	275
4	171
3	90
2	43
1	20
0	11

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite180.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 85

Calls

3 calls:

63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
68.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series277.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
67.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
127.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2504
1	424
0	169

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`*-un-lft-identity` `add-cube-cbrt`
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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

34.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
13.0ms	(/ (sin (* x 0.5)) (sin x))
27.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
46.0ms	(/ (sin (* x 0.5)) (sin x))
138.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify1.8s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3384
1	499
0	181

prune596.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-exp-log`
91×	`times-frac`
68×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
52×	`add-cbrt-cube`
51×	`add-cube-cbrt`
49×	`div-exp`
30×	`prod-exp`
26×	`associate-l`
22×	`cbrt-undiv`
13×	`associate-r`
12×	`cbrt-unprod` `div-inv`
11×	`associate-/r*`
9×	`rec-exp` `1-exp` `associate-/l*`
7×	`pow1`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 197

Calls

4 calls:

11.0ms	(/ 3.0 (* (sin (* 0.5 x)) 8.0))
11.0ms	(/ (sin (* x 0.5)) (sin x))
85.0ms	(* (/ 1 (/ 3.0 (* (sin (* 0.5 x)) 8.0))) (/ (sin (* x 0.5)) (sin x)))
47.0ms	(/ 1 (/ 3.0 (* (sin (* 0.5 x)) 8.0)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 3.0 (* (sin (* 0.5 x)) 8.0))
73.0ms	(/ (sin (* x 0.5)) (sin x))
109.0ms	(* (/ 1 (/ 3.0 (* (sin (* 0.5 x)) 8.0))) (/ (sin (* x 0.5)) (sin x)))
49.0ms	(/ 1 (/ 3.0 (* (sin (* 0.5 x)) 8.0)))

simplify541.0ms

Counts

209 → 209

Iterations

Iter	Nodes
done	5000
1	884
0	303

prune984.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin (* 0.5 x))) (cbrt (sin (* 0.5 x))))
0.7b	(cbrt (sin (* 0.5 x)))
0.7b	(cbrt (sin (* 0.5 x)))
0.7b	(cbrt (sin (* 0.5 x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

28.0ms	(* (cbrt (sin (* 0.5 x))) (cbrt (sin (* 0.5 x))))
5.0ms	(cbrt (sin (* 0.5 x)))
5.0ms	(cbrt (sin (* 0.5 x)))
5.0ms	(cbrt (sin (* 0.5 x)))

series999.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(* (cbrt (sin (* 0.5 x))) (cbrt (sin (* 0.5 x))))
227.0ms	(cbrt (sin (* 0.5 x)))
250.0ms	(cbrt (sin (* 0.5 x)))
248.0ms	(cbrt (sin (* 0.5 x)))

simplify911.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	955
1	237
0	94

prune656.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes83.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.5s	1456×	body	1280	valid
1.2s	1276×	body	640	valid
1.0s	4299×	body	80	valid
810.0ms	635×	body	320	valid
93.0ms	334×	body	160	valid