Details

sample282.0ms

Algorithm

intervals

Results

84.0ms	88×	body	1280	valid
40.0ms	68×	body	640	valid
11.0ms	26×	body	320	valid
9.0ms	68×	body	80	valid
2.0ms	6×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize36.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ r (cos (+ b a)))
0.2b	(* (sin b) (/ r (cos (+ b a))))
4.6b	(cos (+ b a))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

8.0ms	(/ r (cos (+ b a)))
31.0ms	(* (sin b) (/ r (cos (+ b a))))
17.0ms	(cos (+ b a))

series242.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ r (cos (+ b a)))
130.0ms	(* (sin b) (/ r (cos (+ b a))))
41.0ms	(cos (+ b a))

simplify888.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1471
1	277
0	118

prune554.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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:

13.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
62.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
10.0ms	(* (sin a) (sin b))

series789.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
278.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
348.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
55.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	2275
1	445
0	172

prune985.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

13.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
30.0ms	(/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r)
9.0ms	(* (sin b) (sin a))
21.0ms	(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r))

series757.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
169.0ms	(/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r)
72.0ms	(* (sin b) (sin a))
418.0ms	(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin b) (sin a))) r))

simplify1.2s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	3521
1	655
0	248

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b	(* (sin b) (sin a))
0.3b	(pow (* (sin b) (sin a)) 3)
28.9b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
16×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`times-frac`
8×	`cbrt-prod`
6×	`associate-l`
4×	`prod-exp` `cbrt-unprod` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down` `associate-/r/` `unswap-sqr`
2×	`cube-mult` `cbrt-div` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-undiv` `flip3--` `pow1/3` `div-exp` `associate-*r/` `cos-mult` `frac-sub` `rem-cbrt-cube` `div-inv` `flip--`

Counts

4 → 95

Calls

4 calls:

105.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
18.0ms	(* (sin b) (sin a))
13.0ms	(pow (* (sin b) (sin a)) 3)
7.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series574.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
72.0ms	(* (sin b) (sin a))
104.0ms	(pow (* (sin b) (sin a)) 3)
74.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.6s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	2818
1	520
0	189

prune724.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes455.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.9s	2888×	body	1280	valid
1.0s	1804×	body	640	valid
723.0ms	2179×	body	80	valid
460.0ms	782×	body	320	valid
114.0ms	347×	body	160	valid