Details

sample142.0ms

Algorithm

intervals

Results

71.0ms	52×	body	1280	valid
25.0ms	54×	body	640	valid
20.0ms	148×	body	80	valid
7.0ms	23×	body	320	valid
3.0ms	13×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	53
5	53
4	50
3	39
2	31
1	18
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.2b	(* (/ 1.0 (tan B)) x)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
14×	`associate-l`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `prod-exp` `tan-quot` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 101

Calls

4 calls:

28.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
6.0ms	(/ 1.0 (sin B))
7.0ms	(/ 1.0 (tan B))
31.0ms	(* (/ 1.0 (tan B)) x)

series320.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
19.0ms	(/ 1.0 (sin B))
41.0ms	(/ 1.0 (tan B))
127.0ms	(* (/ 1.0 (tan B)) x)

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1607
1	406
0	176

prune658.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
0.1b	(* x (cos B))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`times-frac`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

32.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
12.0ms	(* x (cos B))
8.0ms	(/ 1.0 (sin B))
18.0ms	(/ (* x (cos B)) (sin B))

series313.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
45.0ms	(* x (cos B))
21.0ms	(/ 1.0 (sin B))
99.0ms	(/ (* x (cos B)) (sin B))

simplify1.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1458
1	355
0	150

prune417.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (cos B))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (sin B) (* x (cos B)))
0.3b	(/ 1 (/ (sin B) (* x (cos B))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
34×	`add-sqr-sqrt` `add-exp-log`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv`
7×	`pow1` `div-inv`
5×	`prod-exp`
4×	`add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-r` `associate-l` `cbrt-unprod`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `pow-flip` `inv-pow` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

7.0ms	(* x (cos B))
4.0ms	(/ 1.0 (sin B))
12.0ms	(/ (sin B) (* x (cos B)))
13.0ms	(/ 1 (/ (sin B) (* x (cos B))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* x (cos B))
21.0ms	(/ 1.0 (sin B))
75.0ms	(/ (sin B) (* x (cos B)))
109.0ms	(/ 1 (/ (sin B) (* x (cos B))))

simplify1.2s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	1674
1	451
0	197

prune514.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite35.0ms

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:

26.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
2.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))

series531.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
129.0ms	(cbrt (sin B))
139.0ms	(cbrt (sin B))
141.0ms	(cbrt (sin B))

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	753
1	177
0	75

prune457.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.3s	1710×	body	1280	valid
1.5s	1422×	body	640	valid
1.0s	4905×	body	80	valid
338.0ms	700×	body	320	valid
170.0ms	379×	body	160	valid