Details

sample316.0ms

Algorithm

intervals

Results

37.0ms	88×	body	1280	valid
17.0ms	56×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	73×	body	80	valid
2.0ms	14×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
1.8b	(cos (+ a b))

rewrite31.0ms

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:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series158.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify1.2s

Counts

76 → 76

Iterations

Useful iterations: 3 (339.0ms)

Iter	Nodes	Cost
0	116	909
1	253	883
2	648	793
3	1972	785
done	5000	785

prune210.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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))

rewrite46.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))

series452.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
213.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
47.0ms	(* (sin a) (sin b))

simplify2.1s

Counts

112 → 112

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	170	2072
1	404	2024
2	1175	1834
3	3736	1715
done	5000	1714

prune400.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite26.0ms

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×	`associate-/r/` `cos-mult`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms	(* r (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
6.0ms	(* (sin a) (sin b))

series373.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
37.0ms	(* r (sin b))
212.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
43.0ms	(* (sin a) (sin b))

simplify2.1s

Counts

88 → 88

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	140	1256
1	343	1224
2	1094	1076
3	4113	989
done	5001	988

prune284.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.3b	(pow (* (sin a) (sin b)) 3)
0.3b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.5b	(pow (* (cos a) (cos b)) 3)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
41×	`cos-mult`
36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac` `frac-add`
24×	`add-exp-log` `add-cbrt-cube`
23×	`associate-/r/`
21×	`sin-mult`
20×	`add-cube-cbrt`
19×	`pow-prod-down`
18×	`sqr-pow`
17×	`frac-times` `associate-*r/`
16×	`difference-of-squares`
11×	`associate-*l/`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-/l*`
7×	`flip3-+` `flip-+`
6×	`cube-div` `pow-unpow`
4×	`difference-cubes` `pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `associate-/l/` `distribute-lft-out--` `add-log-exp` `rem-cube-cbrt`
3×	`associate-/r*`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `div-sub` `swap-sqr` `div-exp` `associate-r` `associate-l` `clear-num` `*-commutative` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 162

Calls

4 calls:

55.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))))
3.0ms	(pow (* (sin a) (sin b)) 3)
13.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
3.0ms	(pow (* (cos a) (cos b)) 3)

series535.0ms

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))))
66.0ms	(pow (* (sin a) (sin b)) 3)
57.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
58.0ms	(pow (* (cos a) (cos b)) 3)

simplify1.9s

Counts

174 → 174

Iterations

Useful iterations: 2 (519.0ms)

Iter	Nodes	Cost
0	358	7066
1	1010	6331
2	4834	5859
done	5000	5859

prune738.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes126.0ms

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	25	60
1	33	60
done	33	60

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2856×	body	1280	valid
472.0ms	1780×	body	640	valid
153.0ms	808×	body	320	valid
134.0ms	2181×	body	80	valid
51.0ms	375×	body	160	valid