Details

sample93.0ms

Algorithm

intervals

Results

31.0ms	58×	body	1280	valid
29.0ms	46×	body	640	valid
9.0ms	113×	body	80	valid
7.0ms	28×	body	320	valid
2.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	11	9
done	11	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (cos y)) (* z (sin y)))
0.1b	(* x (cos y))
0.1b	(* z (sin y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 47

Calls

3 calls:

17.0ms	(+ (* x (cos y)) (* z (sin y)))
14.0ms	(* x (cos y))
10.0ms	(* z (sin y))

series228.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(+ (* x (cos y)) (* z (sin y)))
49.0ms	(* x (cos y))
81.0ms	(* z (sin y))

simplify3.1s

Counts

56 → 56

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	81	454
1	184	426
2	457	392
3	1063	392
4	2768	392
done	5001	392

prune233.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos y)) (cbrt (cos y)))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

28.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
2.0ms	(cbrt (cos y))
3.0ms	(cbrt (cos y))
3.0ms	(cbrt (cos y))

series766.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
147.0ms	(cbrt (cos y))
162.0ms	(cbrt (cos y))
145.0ms	(cbrt (cos y))

simplify6.3s

Counts

85 → 85

Iterations

Useful iterations: 4 (3.4s)

Iter	Nodes	Cost
0	64	686
1	122	615
2	336	521
3	1141	499
4	4928	492
done	5001	492

prune392.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (sin y))
0.2b	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
0.3b	(pow (cos y) 2)
0.3b	(cbrt (cos y))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
13×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
9×	`pow1` `associate-r`
6×	`cbrt-prod` `cbrt-unprod`
5×	`pow-exp`
4×	`associate-l` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `pow-unpow`
2×	`pow-prod-down` `*-commutative`
1×	`pow-pow` `unpow1/3` `pow1/3` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

10.0ms	(* z (sin y))
66.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
3.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series663.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* z (sin y))
54.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
24.0ms	(pow (cos y) 2)
534.0ms	(cbrt (cos y))

simplify4.0s

Counts

84 → 84

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	126	759
1	287	658
2	845	582
3	3340	521
done	5000	513

prune333.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt z) (cbrt z))
0.7b	(cbrt z)
0.7b	(cbrt z)
0.7b	(cbrt z)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

11.0ms	(* (cbrt z) (cbrt z))
1.0ms	(cbrt z)
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series1.2s

Counts

4 → 12

Calls

4 calls:

305.0ms	(* (cbrt z) (cbrt z))
328.0ms	(cbrt z)
262.0ms	(cbrt z)
276.0ms	(cbrt z)

simplify5.4s

Counts

85 → 85

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	61	524
1	115	417
2	319	397
3	1092	379
4	4427	374
done	5001	364

prune408.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes196.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	18	17
done	18	17

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.7s	1451×	body	1280	valid
688.0ms	1281×	body	640	valid
594.0ms	4300×	body	80	valid
202.0ms	658×	body	320	valid
72.0ms	310×	body	160	valid