Details

sample488.0ms

Algorithm

intervals

Results

50.0ms	97×	body	1280	valid
17.0ms	51×	body	640	valid
7.0ms	23×	body	320	valid
6.0ms	72×	body	80	valid
2.0ms	13×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite41.0ms

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:

8.0ms	(* r (sin b))
10.0ms	(/ (* r (sin b)) (cos (+ a b)))
10.0ms	(cos (+ a b))

series241.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* r (sin b))
130.0ms	(/ (* r (sin b)) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify2.3s

Counts

56 → 56

Iterations

Iter	Nodes
done	5020
3	2390
2	589
1	211
0	92

prune435.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

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:

11.0ms	(* r (sin b))
14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* (sin a) (sin b))
45.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* r (sin b))
111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
66.0ms	(* (sin a) (sin b))
373.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	4913
2	1129
1	362
0	141

prune757.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

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:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
86.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(* (sin a) (sin b))

series713.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
339.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
190.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
65.0ms	(* (sin a) (sin b))

simplify1.8s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	1483
1	437
0	171

prune930.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize131.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

151×	`sin-mult`
139×	`cos-mult`
109×	`frac-times`
101×	`associate-*r/`
93×	`associate-*l/`
87×	`pow1`
69×	`associate-/l/`
49×	`frac-sub`
37×	`pow-prod-down`
35×	`add-cbrt-cube` `add-exp-log`
29×	`frac-add`
23×	`associate-/r/`
19×	`prod-exp` `cbrt-unprod`
18×	`sub-div`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
9×	`flip3-+` `flip-+`
8×	`pow-sqr` `pow-prod-up`
5×	`associate-r`
4×	`difference-cubes` `pow-plus` `cube-unmult` `pow3` `associate-/l*` `add-log-exp`
3×	`associate-/r` `associate-l` `-commutative`
2×	`pow2` `swap-sqr`
1×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 225

Calls

4 calls:

59.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
90.0ms	(* (* (cos a) (cos b)) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))
879.0ms	(/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos a) (cos b)) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))))
67.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series948.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
155.0ms	(* (* (cos a) (cos b)) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))
602.0ms	(/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))) (+ (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (* (cos a) (cos b)) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))))
107.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify1.7s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
1	1174
0	351

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes494.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.0s	2936×	body	1280	valid
1.6s	1824×	body	640	valid
310.0ms	840×	body	320	valid
235.0ms	2074×	body	80	valid
125.0ms	327×	body	160	valid