Details

sample322.0ms

Algorithm

intervals

Results

138.0ms	94×	body	1280	valid
29.0ms	61×	body	640	valid
9.0ms	73×	body	80	valid
5.0ms	16×	body	320	valid
3.0ms	12×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	243
1	12	243
2	14	243
3	17	243
4	19	243
5	20	243
done	20	243

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize39.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite672.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

18.0ms	(* r (sin b))
20.0ms	(/ (* r (sin b)) (cos (+ a b)))
20.0ms	(cos (+ a b))

series396.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(* r (sin b))
247.0ms	(/ (* r (sin b)) (cos (+ a b)))
39.0ms	(cos (+ a b))

simplify3.6s

Counts

56 → 56

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	92	13369
1	211	12453
2	589	12293
3	2390	12053
done	5020	11973

prune370.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

16.0ms	(* (cos a) (cos b))
33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* (sin a) (sin b))
25.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos a) (cos b))
119.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
66.0ms	(* (sin a) (sin b))
311.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify137.0ms

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	156	33289