Details

sample252.0ms

Algorithm

intervals

Results

80.0ms	96×	body	1280	valid
33.0ms	61×	body	640	valid
10.0ms	67×	body	80	valid
9.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.9b	(cos (+ a b))

rewrite31.0ms

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:

7.0ms	(* r (sin b))
10.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series195.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* r (sin b))
114.0ms	(/ (* r (sin b)) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify637.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
2	870
1	211
0	92

prune294.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

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))
0.3b	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

rewrite76.0ms

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:

27.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
10.0ms	(* (sin a) (sin b))
28.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
45.0ms	(* r (sin b))
69.0ms	(* (sin a) (sin b))
329.0ms	(/ (* 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

prune673.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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

rewrite266.0ms

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:

92.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
14.0ms	(/ (sin b) (cos a))
22.0ms	(/ (cos b) (/ (sin b) (cos a)))
116.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
53.0ms	(/ (sin b) (cos a))
80.0ms	(/ (cos b) (/ (sin b) (cos a)))
258.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))

simplify1.5s

Counts

207 → 207

Iterations

Iter	Nodes
done	5001
2	3879
1	769
0	348

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

66.0ms	(- (* (/ 1 (sin b)) (* (cos b) (cos a))) (/ (sin a) 1))
10.0ms	(/ 1 (sin b))
80.0ms	(/ r (- (* (/ 1 (sin b)) (* (cos b) (cos a))) (/ (sin a) 1)))
46.0ms	(* (/ 1 (sin b)) (* (cos b) (cos a)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(- (* (/ 1 (sin b)) (* (cos b) (cos a))) (/ (sin a) 1))
28.0ms	(/ 1 (sin b))
326.0ms	(/ r (- (* (/ 1 (sin b)) (* (cos b) (cos a))) (/ (sin a) 1)))
125.0ms	(* (/ 1 (sin b)) (* (cos b) (cos a)))

simplify1.8s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	3273
1	550
0	214

prune625.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes341.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
2	22
1	20
0	14

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.4s	2845×	body	1280	valid
1.2s	1942×	body	640	valid
382.0ms	2101×	body	80	valid
285.0ms	354×	body	160	valid
258.0ms	759×	body	320	valid