Details

sample234.0ms

Algorithm

intervals

Results

62.0ms	22×	body	320	valid
56.0ms	79×	body	1280	valid
25.0ms	67×	body	640	valid
9.0ms	77×	body	80	valid
2.0ms	11×	body	160	valid

simplify35.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite116.0ms

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×	`associate-l` `associate-/r` `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 → 67

Calls

3 calls:

63.0ms	(* r (/ (sin b) (cos (+ a b))))
21.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

series219.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(* r (/ (sin b) (cos (+ a b))))
46.0ms	(/ (sin b) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify5.4s

Counts

76 → 76

Iterations

Useful iterations: 4 (3.7s)

Iter	Nodes	Cost
0	116	909
1	249	883
2	638	793
3	1727	785
4	4912	783
done	5000	783

prune329.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))

rewrite271.0ms

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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
154.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
64.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
24.0ms	(* (sin a) (sin b))

series760.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
322.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
215.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms	(* (sin a) (sin b))

simplify2.6s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1160	1838
3	3364	1715
done	5000	1715

prune638.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (- (* (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)
26.7b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

44.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
23.0ms	(* (sin b) (sin a))
19.0ms	(pow (* (sin b) (sin a)) 3)
10.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series411.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
64.0ms	(* (sin b) (sin a))
84.0ms	(pow (* (sin b) (sin a)) 3)
55.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.2s

Counts

102 → 102

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	163	1550
1	343	1265
2	1199	1175
done	5001	1152

prune680.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

32.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
41.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))
127.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
138.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
58.0ms	(* (sin a) (sin b))
363.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify4.7s

Counts

122 → 122

Iterations

Useful iterations: 3 (2.6s)

Iter	Nodes	Cost
0	181	2272
1	461	2088
2	1440	1834
3	4904	1768
done	5001	1768

prune497.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes195.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	19
1	18	19
done	18	19

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.2s	2908×	body	1280	valid
1.3s	1810×	body	640	valid
389.0ms	766×	body	320	valid
339.0ms	2127×	body	80	valid
146.0ms	392×	body	160	valid