Details

sample1.1s

Algorithm

intervals

Results

76.0ms	94×	body	1280	valid
32.0ms	61×	body	640	valid
11.0ms	73×	body	80	valid
5.0ms	16×	body	320	valid
3.0ms	12×	body	160	valid

simplify48.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize43.0ms

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))

rewrite83.0ms

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×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

17.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

series290.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* r (sin b))
192.0ms	(/ (* r (sin b)) (cos (+ a b)))
46.0ms	(cos (+ a b))

simplify3.2s

Counts

62 → 62

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	98	14743
1	216	13752
2	667	13432
3	2951	13402
done	5051	13352

prune412.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

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))))

rewrite91.0ms

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

Counts

4 → 87

Calls

4 calls:

16.0ms	(* (cos a) (cos b))
28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms	(* (sin a) (sin b))
22.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos a) (cos b))
116.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
75.0ms	(* (sin a) (sin b))
347.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify148.0ms

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	168	37023