Details

sample202.0ms

Algorithm

intervals

Results

49.0ms	89×	body	1280	valid
19.0ms	52×	body	640	valid
9.0ms	33×	body	320	valid
5.0ms	69×	body	80	valid
2.0ms	13×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 67

Calls

3 calls:

16.0ms	(* r (/ (sin b) (cos (+ a b))))
9.0ms	(/ (sin b) (cos (+ a b)))
11.0ms	(cos (+ a b))

series356.0ms

Counts

3 → 9

Calls

3 calls:

274.0ms	(* r (/ (sin b) (cos (+ a b))))
44.0ms	(/ (sin b) (cos (+ a b)))
38.0ms	(cos (+ a b))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	3075
2	838
1	269
0	117

prune555.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 100

Calls

4 calls:

86.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms	(* (sin a) (sin b))
23.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
116.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
86.0ms	(* (sin a) (sin b))
201.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.2s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4737
2	1464
1	438
0	171

prune914.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin b) (cos a))
0.1b	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
0.2b	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
0.2b	(/ (cos b) (/ (sin b) (cos a)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
111×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
66×	`add-cube-cbrt`
23×	`associate-/r*`
15×	`difference-of-squares`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`pow1`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 158

Calls

4 calls:

8.0ms	(/ (sin b) (cos a))
61.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
93.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
30.0ms	(/ (cos b) (/ (sin b) (cos a)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sin b) (cos a))
118.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
308.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
107.0ms	(/ (cos b) (/ (sin b) (cos a)))

simplify1.8s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	1925
1	639
0	281

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ 1 (/ (/ (sin b) (cos a)) (cos b))) (sin a))
0.2b	(/ r (- (/ 1 (/ (/ (sin b) (cos a)) (cos b))) (sin a)))
0.2b	(/ (/ (sin b) (cos a)) (cos b))
0.2b	(/ 1 (/ (/ (sin b) (cos a)) (cos b)))

rewrite810.0ms

Algorithm

rewrite-expression-head

Rules

564×	`times-frac`
362×	`add-sqr-sqrt`
277×	`*-un-lft-identity`
247×	`add-cube-cbrt`
58×	`associate-/r*`
35×	`difference-of-squares`
32×	`add-exp-log`
28×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp` `associate-/l*`
10×	`cbrt-undiv` `distribute-lft-out--`
6×	`add-log-exp`
5×	`pow1`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/r/`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 356

Calls

4 calls:

531.0ms	(- (/ 1 (/ (/ (sin b) (cos a)) (cos b))) (sin a))
173.0ms	(/ r (- (/ 1 (/ (/ (sin b) (cos a)) (cos b))) (sin a)))
26.0ms	(/ (/ (sin b) (cos a)) (cos b))
36.0ms	(/ 1 (/ (/ (sin b) (cos a)) (cos b)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (/ 1 (/ (/ (sin b) (cos a)) (cos b))) (sin a))
303.0ms	(/ r (- (/ 1 (/ (/ (sin b) (cos a)) (cos b))) (sin a)))
118.0ms	(/ (/ (sin b) (cos a)) (cos b))
97.0ms	(/ 1 (/ (/ (sin b) (cos a)) (cos b)))

simplify2.8s

Counts

368 → 368

Iterations

Iter	Nodes
done	5000
2	3529
1	1445
0	580

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes435.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.9s	2858×	body	1280	valid
995.0ms	1820×	body	640	valid
758.0ms	797×	body	320	valid
398.0ms	2173×	body	80	valid
147.0ms	352×	body	160	valid