Details

sample161.0ms

Algorithm

intervals

Results

78.0ms	57×	body	1280	valid
31.0ms	47×	body	640	valid
21.0ms	150×	body	80	valid
11.0ms	18×	body	320	valid
5.0ms	14×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	52
6	52
5	50
4	44
3	37
2	31
1	18
0	10

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`times-frac` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`clear-num` `frac-2neg` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `tan-quot` `associate-/r/` `frac-sub` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

24.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
4.0ms	(/ 1.0 (sin B))
15.0ms	(/ (* x 1.0) (tan B))

series281.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
26.0ms	(/ 1.0 (sin B))
126.0ms	(/ (* x 1.0) (tan B))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1078
1	338
0	144

prune395.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
14×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `tan-quot` `associate-*r/` `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:

19.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
4.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
17.0ms	(* x (/ 1.0 (tan B)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
25.0ms	(/ 1.0 (sin B))
39.0ms	(/ 1.0 (tan B))
120.0ms	(* x (/ 1.0 (tan B)))

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1234
1	403
0	175

prune597.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* 1.0 (* (cos B) x)) (sin B)))
0.1b	(* (cos B) x)
0.1b	(/ 1.0 (sin B))
0.3b	(/ (* 1.0 (* (cos B) x)) (sin B))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

32.0ms	(- (/ 1.0 (sin B)) (/ (* 1.0 (* (cos B) x)) (sin B)))
11.0ms	(* (cos B) x)
7.0ms	(/ 1.0 (sin B))
28.0ms	(/ (* 1.0 (* (cos B) x)) (sin B))

series372.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(- (/ 1.0 (sin B)) (/ (* 1.0 (* (cos B) x)) (sin B)))
58.0ms	(* (cos B) x)
31.0ms	(/ 1.0 (sin B))
116.0ms	(/ (* 1.0 (* (cos B) x)) (sin B))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1414
1	407
0	165

prune644.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
35.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt (/ 1.0 (sin B)))
161.0ms	(cbrt (/ 1.0 (sin B)))
175.0ms	(cbrt (/ 1.0 (sin B)))
201.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify1.8s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
3	1936
2	782
1	333
0	170

prune914.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes110.0ms

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

sample5.9s

Algorithm

intervals

Results

2.0s	1763×	body	1280	valid
1.5s	4879×	body	80	valid
1.5s	1421×	body	640	valid
466.0ms	750×	body	320	valid
114.0ms	357×	body	160	valid