Details

sample100.0ms

Algorithm

intervals

Results

40.0ms	53×	body	1280	valid
17.0ms	42×	body	640	valid
13.0ms	127×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	9×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

15.0ms	(- (* x (cos y)) (* z (sin y)))
14.0ms	(* z (sin y))
14.0ms	(* x (cos y))

series269.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(- (* x (cos y)) (* z (sin y)))
82.0ms	(* z (sin y))
67.0ms	(* x (cos y))

simplify3.8s

Counts

57 → 57

Iterations

Iter	Nodes
done	5021
4	4873
3	1340
2	420
1	178
0	80

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

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))

rewrite31.0ms

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×	`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:

21.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))

series784.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
193.0ms	(cbrt (cos y))
179.0ms	(cbrt (cos y))
182.0ms	(cbrt (cos y))

simplify1.8s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	1140
2	366
1	144
0	64

prune529.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
15×	`pow1`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`add-cbrt-cube` `associate-r` `prod-exp`
7×	`associate-l` `cbrt-unprod`
6×	`cbrt-prod`
4×	`add-log-exp`
3×	`swap-sqr` `pow-prod-down` `*-commutative`
2×	`pow-exp` `unswap-sqr`
1×	`pow2` `pow-to-exp` `sqr-cos` `pow-plus` `unpow1/3` `pow1/3` `pow-sqr` `cos-mult` `pow-prod-up`

Counts

4 → 80

Calls

4 calls:

8.0ms	(* z (sin y))
31.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
13.0ms	(* (cos y) (cos y))
1.0ms	(cbrt (cos y))

series310.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* z (sin y))
57.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
25.0ms	(* (cos y) (cos y))
143.0ms	(cbrt (cos y))

simplify2.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	3388
2	1043
1	346
0	134

prune652.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (sin y))
0.2b	(* (* x (pow (+ 1/2 (* 1/2 (cos (+ y y)))) 1/3)) (cbrt (cos y)))
0.3b	(cbrt (cos y))
0.4b	(+ 1/2 (* 1/2 (cos (+ y y))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
11×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
8×	`pow1` `prod-exp`
6×	`cbrt-prod` `cbrt-unprod` `add-log-exp`
4×	`associate-l`
2×	`pow-prod-down` `*-commutative`
1×	`pow-to-exp` `+-commutative` `sum-log` `flip3-+` `unpow1/3` `pow1/3` `pow-exp` `flip-+` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

15.0ms	(* z (sin y))
61.0ms	(* (* x (pow (+ 1/2 (* 1/2 (cos (+ y y)))) 1/3)) (cbrt (cos y)))
1.0ms	(cbrt (cos y))
5.0ms	(+ 1/2 (* 1/2 (cos (+ y y))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* z (sin y))
252.0ms	(* (* x (pow (+ 1/2 (* 1/2 (cos (+ y y)))) 1/3)) (cbrt (cos y)))
157.0ms	(cbrt (cos y))
54.0ms	(+ 1/2 (* 1/2 (cos (+ y y))))

simplify3.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
3	4323
2	1063
1	340
0	131

prune534.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes556.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1456×	body	1280	valid
1.2s	1264×	body	640	valid
562.0ms	4318×	body	80	valid
250.0ms	618×	body	320	valid
70.0ms	344×	body	160	valid