Details

sample398.0ms

Algorithm

intervals

Results

37.0ms	87×	body	1280	valid
13.0ms	53×	body	640	valid
6.0ms	75×	body	80	valid
4.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
2.9b	(cos (+ a b))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

10.0ms	(/ (sin b) (cos (+ a b)))
17.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(cos (+ a b))

series172.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (sin b) (cos (+ a b)))
101.0ms	(* r (/ (sin b) (cos (+ a b))))
31.0ms	(cos (+ a b))

simplify2.2s

Counts

82 → 82

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	666	834
3	1809	830
done	5001	824

prune223.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
71.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
48.0ms	(* (sin a) (sin b))
223.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
119.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7s

Counts

122 → 122

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1248	1955
3	3717	1826
done	5000	1821

prune381.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))
12.0ms	(* (sin a) (sin b))
29.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
40.0ms	(* r (sin b))
46.0ms	(* (sin a) (sin b))
229.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	152	1364
1	370	1324
2	1166	1174
3	4192	1081
done	5002	1078

prune300.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`fma-neg`
6×	`pow1` `div-inv` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 128

Calls

4 calls:

11.0ms	(* (cos b) (cos a))
27.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
13.0ms	(/ (* (cos b) (cos a)) (sin b))
31.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos b) (cos a))
89.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
63.0ms	(/ (* (cos b) (cos a)) (sin b))
195.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify1.0s

Counts

140 → 140

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	213	2538
1	455	2227
2	1268	1949
done	5001	1820

prune344.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes145.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2872×	body	1280	valid
426.0ms	1763×	body	640	valid
151.0ms	796×	body	320	valid
128.0ms	2210×	body	80	valid
44.0ms	361×	body	160	valid