Details

sample398.0ms

Algorithm

intervals

Results

130.0ms	93×	body	1280	valid
107.0ms	61×	body	640	valid
18.0ms	26×	body	320	valid
14.0ms	68×	body	80	valid
4.0ms	8×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite46.0ms

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` `insert-posit16` `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 → 70

Calls

3 calls:

15.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
11.0ms	(cos (+ a b))

series180.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(* r (/ (sin b) (cos (+ a b))))
46.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify1.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	2008
3	2008
2	844
1	271
0	120

prune915.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

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

rewrite191.0ms

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`
4×	`insert-posit16`
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 → 104

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
102.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
22.0ms	(* (sin a) (sin b))
48.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
301.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
60.0ms	(* (sin a) (sin b))
154.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

116 → 116

Iterations

Iter	Nodes
done	2010
3	2010
2	1468
1	439
0	175

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b)))
0.3b	(/ (- (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

237×	`pow1`
165×	`cos-mult`
129×	`sin-mult`
111×	`frac-times`
103×	`pow-prod-down`
101×	`associate-*r/`
97×	`associate-*l/`
71×	`add-cbrt-cube` `add-exp-log`
69×	`associate-/l/`
49×	`frac-sub`
47×	`prod-exp` `cbrt-unprod`
42×	`pow-prod-up`
27×	`frac-add`
23×	`associate-/r/`
21×	`pow-plus`
20×	`pow-sqr`
18×	`sub-div`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
7×	`flip3-+` `flip-+`
5×	`pow2` `pow3`
4×	`difference-cubes` `cube-unmult` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-l` `-commutative`
2×	`swap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 283

Calls

4 calls:

220.0ms	(* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b)))
884.0ms	(/ (- (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
62.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
59.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b)))
560.0ms	(/ (- (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
83.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
74.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify1.7s

Counts

295 → 295

Iterations

Iter	Nodes
done	2000
2	2000
1	1079
0	330

prune6.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`associate-r`
20×	`times-frac`
14×	`pow1` `prod-exp`
9×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`associate-*r/` `cos-mult` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `-commutative` `associate-/l*`
2×	`flip3--` `un-div-inv` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 122

Calls

4 calls:

96.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
51.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))
128.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
162.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms	(* (sin a) (sin b))
145.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.4s

Counts

134 → 134

Iterations

Iter	Nodes
done	2015
3	2015
2	1643
1	495
0	195

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes261.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	14

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.1s	2814×	body	1280	valid
1.7s	1909×	body	640	valid
497.0ms	2107×	body	80	valid
496.0ms	790×	body	320	valid
133.0ms	383×	body	160	valid