Details

sample263.0ms

Algorithm

intervals

Results

84.0ms	94×	body	1280	valid
66.0ms	73×	body	80	valid
37.0ms	61×	body	640	valid
6.0ms	16×	body	320	valid
4.0ms	12×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	243
1	12	243
2	16	243
3	18	243
4	20	243
5	21	243
done	21	243

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.1b	(cos (+ a b))

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×	`expm1-log1p-u` `associate-/r` `associate-l` `log1p-expm1-u` `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 → 73

Calls

3 calls:

30.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(/ (sin b) (cos (+ a b)))
22.0ms	(cos (+ a b))

series252.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(* r (/ (sin b) (cos (+ a b))))
47.0ms	(/ (sin b) (cos (+ a b)))
38.0ms	(cos (+ a b))

simplify3.2s

Counts

82 → 82

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	123	25254
1	280	23531
2	879	23330
3	3284	23075
done	5012	23010

prune641.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (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))))

rewrite146.0ms

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×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 110

Calls

4 calls:

14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
74.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
20.0ms	(* (sin a) (sin b))
34.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series777.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
390.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
85.0ms	(* (sin a) (sin b))
144.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify211.0ms

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	182	55979