Details

sample176.0ms

Algorithm

intervals

Results

55.0ms	50×	body	1280	valid
51.0ms	135×	body	80	valid
34.0ms	42×	body	640	valid
11.0ms	20×	body	320	valid
4.0ms	9×	body	160	valid

simplify394.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite344.0ms

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

Counts

3 → 85

Calls

3 calls:

138.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
59.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
141.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series294.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
55.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
148.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.8s

Counts

94 → 94

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	169	1554
1	424	1349
2	2490	1130
done	5002	1088

prune399.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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

rewrite178.0ms

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

Counts

3 → 104

Calls

3 calls:

17.0ms	(/ (sin (* x 0.5)) (sin x))
108.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
48.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series286.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (sin (* x 0.5)) (sin x))
149.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
59.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify3.4s

Counts

113 → 113

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	189	1786
1	499	1739
2	3314	1390
done	5001	1349

prune525.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
27×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-l` `associate-l/` `-commutative`

Counts

3 → 99

Calls

3 calls:

25.0ms	(/ (sin (* 0.5 x)) 3.0)
15.0ms	(/ (sin (* x 0.5)) (sin x))
57.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (sin (* 0.5 x)) 3.0)
88.0ms	(/ (sin (* x 0.5)) (sin x))
135.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify2.0s

Counts

108 → 108

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	193	1725
1	481	1656
2	2894	1361
done	5000	1310

prune379.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))) (/ (sin (* x 0.5)) (sin x)))
0.2b	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0))))
0.4b	(* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))
1.0b	(/ (cbrt 8.0) (cbrt 3.0))

rewrite712.0ms

Algorithm

rewrite-expression-head

Rules

268×	`add-exp-log`
162×	`add-cbrt-cube`
145×	`prod-exp` `cbrt-unprod`
86×	`times-frac`
82×	`cbrt-prod`
80×	`add-sqr-sqrt`
69×	`cbrt-undiv` `div-exp`
66×	`add-cube-cbrt` `*-un-lft-identity`
54×	`associate-r`
20×	`pow1`
11×	`associate-*r/`
10×	`pow-prod-down`
9×	`associate-l`
6×	`frac-times` `associate-l/` `associate-/r` `associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`*-commutative`
1×	`frac-2neg` `clear-num`

Counts

4 → 275

Calls

4 calls:

437.0ms	(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))) (/ (sin (* x 0.5)) (sin x)))
187.0ms	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0))))
58.0ms	(* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))
9.0ms	(/ (cbrt 8.0) (cbrt 3.0))

series997.0ms

Counts

4 → 10

Calls

4 calls:

476.0ms	(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))) (/ (sin (* x 0.5)) (sin x)))
339.0ms	(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0))))
182.0ms	(* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))
0.0ms	(/ (cbrt 8.0) (cbrt 3.0))

simplify740.0ms

Counts

285 → 285

Iterations

Useful iterations: done (730.0ms)

Iter	Nodes	Cost
0	403	8131
1	1292	7668
done	5000	4918

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	15	16
done	15	16

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.3s	1543×	body	1280	valid
902.0ms	1255×	body	640	valid
647.0ms	4291×	body	80	valid
382.0ms	621×	body	320	valid
86.0ms	290×	body	160	valid