Details

sample123.0ms

Algorithm

intervals

Results

50.0ms	65×	body	1280	valid
26.0ms	154×	body	80	valid
21.0ms	43×	body	640	valid
7.0ms	23×	body	320	valid
2.0ms	7×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	10	358
1	18	358
2	33	318
3	41	318
4	48	318
5	54	318
6	56	318
done	56	318

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-r`
13×	`add-cbrt-cube` `fma-neg` `prod-diff` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`clear-num` `frac-2neg` `prod-exp` `tan-quot` `associate-*r/` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 135

Calls

4 calls:

55.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
6.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
15.0ms	(* x (/ 1.0 (tan B)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
23.0ms	(/ 1.0 (sin B))
47.0ms	(/ 1.0 (tan B))
170.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	200	45976
1	473	43936
2	1510	42711
done	5011	42494

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
0.1b	(/ 1.0 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `fma-neg` `prod-diff` `add-exp-log`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

51.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
8.0ms	(/ 1.0 (sin B))
13.0ms	(* x (cos B))
19.0ms	(/ (* x (cos B)) (sin B))

series466.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
32.0ms	(/ 1.0 (sin B))
61.0ms	(* x (cos B))
174.0ms	(/ (* x (cos B)) (sin B))

simplify1.8s

Counts

127 → 127

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	175	40753
1	421	39193
2	1305	38331
done	5008	37879

prune852.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
28×	`times-frac`
22×	`add-cbrt-cube` `add-exp-log`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r/` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

8.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (sin B))
26.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
29.0ms	(* x (/ 1.0 (sin B)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1.0 (sin B))
22.0ms	(/ 1.0 (sin B))
156.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
88.0ms	(* x (/ 1.0 (sin B)))

simplify4.4s

Counts

127 → 127

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	140	30577
1	341	28729
2	1145	28245
3	4261	28165
done	5003	27605

prune730.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (* x (cos B)) (sin B)))
0.5b	(cbrt (/ (* x (cos B)) (sin B)))
0.5b	(cbrt (/ (* x (cos B)) (sin B)))
0.5b	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

53×	`cbrt-prod`
30×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

3.0ms	(cbrt (/ (* x (cos B)) (sin B)))
3.0ms	(cbrt (/ (* x (cos B)) (sin B)))
3.0ms	(cbrt (/ (* x (cos B)) (sin B)))
19.0ms	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))

series1.1s

Counts

4 → 12

Calls

4 calls:

290.0ms	(cbrt (/ (* x (cos B)) (sin B)))
276.0ms	(cbrt (/ (* x (cos B)) (sin B)))
276.0ms	(cbrt (/ (* x (cos B)) (sin B)))
289.0ms	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))

simplify125.0ms

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	135	53684