Details

sample215.0ms

Algorithm

intervals

Results

71.0ms	303×	body	80	nan
37.0ms	58×	body	1280	valid
18.0ms	173×	body	80	valid
13.0ms	29×	body	640	valid
12.0ms	12×	body	2560	valid
4.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify349.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	19
1	32	19
2	54	19
3	75	19
4	87	19
5	89	19
done	89	19

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
0.4b	(/ (* z t) 3.0)
26.2b	(cos (- y (/ (* z t) 3.0)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`cos-sum` `frac-2neg` `clear-num` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 72

Calls

4 calls:

13.0ms	(/ a (* b 3.0))
46.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
11.0ms	(/ (* z t) 3.0)
18.0ms	(cos (- y (/ (* z t) 3.0)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ a (* b 3.0))
144.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
29.0ms	(/ (* z t) 3.0)
40.0ms	(cos (- y (/ (* z t) 3.0)))

simplify3.0s

Counts

84 → 84

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	170	993
1	399	961
2	1339	813
3	4829	813
done	5000	813

prune380.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))
0.3b	(/ t (sqrt 3.0))
0.3b	(/ z (sqrt 3.0))
25.9b	(cos (- y (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
84×	`times-frac`
60×	`add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
22×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`unswap-sqr`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`cos-sum` `frac-2neg` `clear-num`
1×	`cos-diff` `frac-times` `sub-neg` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 161

Calls

4 calls:

51.0ms	(* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))
6.0ms	(/ t (sqrt 3.0))
6.0ms	(/ z (sqrt 3.0))
10.0ms	(cos (- y (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))))

series558.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))
84.0ms	(/ t (sqrt 3.0))
69.0ms	(/ z (sqrt 3.0))
223.0ms	(cos (- y (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))))

simplify1.7s

Counts

173 → 173

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	197	2006
1	463	1849
2	1442	1619
done	5001	1553

prune843.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 16.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
26.1b	(cos (- y (* (/ z (sqrt 3.0)) (* (* (/ (cbrt t) (sqrt (sqrt 3.0))) (cbrt t)) (/ (cbrt t) (sqrt (sqrt 3.0)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
14.0ms	(cos (- y (* (/ z (sqrt 3.0)) (* (* (/ (cbrt t) (sqrt (sqrt 3.0))) (cbrt t)) (/ (cbrt t) (sqrt (sqrt 3.0)))))))

series937.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(cbrt t)
224.0ms	(cbrt t)
220.0ms	(cbrt t)
241.0ms	(cos (- y (* (/ z (sqrt 3.0)) (* (* (/ (cbrt t) (sqrt (sqrt 3.0))) (cbrt t)) (/ (cbrt t) (sqrt (sqrt 3.0)))))))

simplify3.1s

Counts

55 → 55

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	64	628
1	116	614
2	267	486
3	831	309
4	4134	309
done	5001	309

prune488.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 16.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin (- (* z (/ t 3.0)))))
0.3b	(* (* 2.0 (sqrt x)) (- (* (cos (* z (/ t 3.0))) (cos y)) (* (sin y) (sin (- (* z (/ t 3.0)))))))
29.5b	(cos (* z (/ t 3.0)))
29.8b	(sin (- (* z (/ t 3.0))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sin-mult`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sin-neg` `cos-mult` `*-commutative`
1×	`neg-sub0` `flip3--` `sin-diff` `distribute-rgt-neg-out` `frac-sub` `flip--` `sub-div` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

27.0ms	(* (sin y) (sin (- (* z (/ t 3.0)))))
144.0ms	(* (* 2.0 (sqrt x)) (- (* (cos (* z (/ t 3.0))) (cos y)) (* (sin y) (sin (- (* z (/ t 3.0)))))))
10.0ms	(cos (* z (/ t 3.0)))
15.0ms	(sin (- (* z (/ t 3.0))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sin y) (sin (- (* z (/ t 3.0)))))
297.0ms	(* (* 2.0 (sqrt x)) (- (* (cos (* z (/ t 3.0))) (cos y)) (* (sin y) (sin (- (* z (/ t 3.0)))))))
15.0ms	(cos (* z (/ t 3.0)))
33.0ms	(sin (- (* z (/ t 3.0))))

simplify1.4s

Counts

74 → 74

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	153	1540
1	389	1488
2	1374	1256
done	5000	1216

prune463.0ms

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 15.9b

regimes4.5s

Accuracy

47% (2.5b remaining)

Error of 17.9b against oracle of 15.4b and baseline of 20.1b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	42	86
1	55	69
done	55	69

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.7s	9102×	body	80	nan
1.1s	1543×	body	1280	valid
1.0s	5701×	body	80	valid
774.0ms	926×	body	640	valid
448.0ms	390×	body	2560	valid
197.0ms	416×	body	320	valid
42.0ms	192×	body	160	valid