Details

sample241.0ms

Algorithm

intervals

Results

125.0ms	91×	body	1280	valid
29.0ms	60×	body	640	valid
13.0ms	31×	body	320	valid
7.0ms	65×	body	80	valid
2.0ms	9×	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

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize79.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite133.0ms

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:

47.0ms	(* r (sin b))
59.0ms	(/ (* r (sin b)) (cos (+ a b)))
22.0ms	(cos (+ a b))

series204.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
129.0ms	(/ (* r (sin b)) (cos (+ a b)))
33.0ms	(cos (+ a b))

simplify2.5s

Counts

56 → 56

Iterations

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

prune368.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

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:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(* r (sin b))
20.0ms	(* (sin a) (sin b))
28.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* r (sin b))
84.0ms	(* (sin a) (sin b))
336.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1201
1	361
0	141

prune779.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

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))

rewrite148.0ms

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:

27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
20.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series626.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
323.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
138.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
59.0ms	(* (sin a) (sin b))

simplify2.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	1483
1	437
0	171

prune987.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

17.0ms	(* (cos b) (cos a))
33.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
24.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))
11.0ms	(/ (* (cos b) (cos a)) (sin b))

series584.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos b) (cos a))
125.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
292.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))
105.0ms	(/ (* (cos b) (cos a)) (sin b))

simplify2.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5067
3	4500
2	1137
1	386
0	175

prune850.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

regimes348.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	2868×	body	1280	valid
2.0s	1875×	body	640	valid
349.0ms	768×	body	320	valid
268.0ms	2150×	body	80	valid
74.0ms	339×	body	160	valid