Details

sample536.0ms

Algorithm

intervals

Results

243.0ms	96×	body	1280	valid
38.0ms	63×	body	640	valid
9.0ms	70×	body	80	valid
9.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
4	20
3	19
2	16
1	12
0	8

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

14.0ms	(* r (sin b))
18.0ms	(/ (* r (sin b)) (cos (+ a b)))
18.0ms	(cos (+ a b))

series495.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms	(* r (sin b))
296.0ms	(/ (* r (sin b)) (cos (+ a b)))
42.0ms	(cos (+ a b))

simplify756.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
2	870
1	211
0	92

prune231.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

13.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
23.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series534.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
50.0ms	(* r (sin b))
67.0ms	(* (sin a) (sin b))
319.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1711
1	369
0	146

prune630.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
0.1b	(/ (sin b) (cos a))
0.2b	(/ (cos b) (/ (sin b) (cos a)))
0.3b	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

223×	`add-sqr-sqrt`
211×	`times-frac`
118×	`*-un-lft-identity`
73×	`add-cube-cbrt`
45×	`difference-of-squares`
30×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out--`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/r/`
3×	`clear-num` `frac-2neg`
2×	`flip3--` `frac-sub` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 195

Calls

4 calls:

79.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
13.0ms	(/ (sin b) (cos a))
18.0ms	(/ (cos b) (/ (sin b) (cos a)))
125.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))

series611.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
67.0ms	(/ (sin b) (cos a))
80.0ms	(/ (cos b) (/ (sin b) (cos a)))
310.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))

simplify1.4s

Counts

207 → 207

Iterations

Iter	Nodes
done	5001
2	3879
1	769
0	348

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin b) (cos a))
0.2b	(/ (cos b) (/ (sin b) (cos a)))
0.2b	(* r (/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a))))
0.3b	(/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

149×	`times-frac`
148×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
78×	`add-cube-cbrt`
27×	`associate-r`
24×	`add-exp-log`
23×	`associate-/r*`
21×	`difference-of-squares`
18×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp` `div-inv`
7×	`pow1` `distribute-lft-out--`
6×	`cbrt-undiv`
5×	`associate-/r/`
4×	`prod-exp` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `unswap-sqr`
2×	`rec-exp` `flip3--` `1-exp` `cbrt-unprod` `flip--`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 196

Calls

4 calls:

7.0ms	(/ (sin b) (cos a))
11.0ms	(/ (cos b) (/ (sin b) (cos a)))
116.0ms	(* r (/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a))))
50.0ms	(/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (sin b) (cos a))
96.0ms	(/ (cos b) (/ (sin b) (cos a)))
219.0ms	(* r (/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a))))
119.0ms	(/ 1 (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))

simplify1.5s

Counts

208 → 208

Iterations

Iter	Nodes
done	5001
2	3643
1	786
0	319

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes365.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.7s	2945×	body	1280	valid
1.3s	1803×	body	640	valid
515.0ms	367×	body	160	valid
304.0ms	2112×	body	80	valid
241.0ms	773×	body	320	valid