Details

sample139.0ms

Algorithm

intervals

Results

66.0ms	65×	body	1280	valid
26.0ms	43×	body	640	valid
20.0ms	154×	body	80	valid
10.0ms	23×	body	320	valid
2.0ms	7×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	10	358
1	18	358
2	31	318
3	37	318
4	44	318
5	50	318
6	52	318
done	52	318

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
14×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
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 → 101

Calls

4 calls:

25.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
4.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
15.0ms	(* x (/ 1.0 (tan B)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
40.0ms	(/ 1.0 (sin B))
51.0ms	(/ 1.0 (tan B))
200.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

113 → 113

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	175	31187
1	403	29392
2	1234	28907
done	5000	28747

prune691.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 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))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`times-frac`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
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 → 81

Calls

4 calls:

34.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
9.0ms	(/ 1.0 (sin B))
13.0ms	(* x (cos B))
18.0ms	(/ (* x (cos B)) (sin B))

series412.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
42.0ms	(/ 1.0 (sin B))
45.0ms	(* x (cos B))
115.0ms	(/ (* x (cos B)) (sin B))

simplify1.9s

Counts

93 → 93

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	150	24221
1	353	22963
2	1138	22439
done	5001	22399

prune575.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)))

rewrite86.0ms

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×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r/` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 107

Calls

4 calls:

5.0ms	(/ 1.0 (sin B))
9.0ms	(/ 1.0 (sin B))
51.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
18.0ms	(* x (/ 1.0 (sin B)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (sin B))
21.0ms	(/ 1.0 (sin B))
172.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
64.0ms	(* x (/ 1.0 (sin B)))

simplify3.9s

Counts

119 → 119

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	134	28757
1	329	26952
2	1125	26550
3	4405	26390
done	5000	25910

prune649.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

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))))

rewrite48.0ms

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×	`add-cbrt-cube` `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 → 103

Calls

4 calls:

6.0ms	(cbrt (/ (* x (cos B)) (sin B)))
6.0ms	(cbrt (/ (* x (cos B)) (sin B)))
6.0ms	(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:

268.0ms	(cbrt (/ (* x (cos B)) (sin B)))
212.0ms	(cbrt (/ (* x (cos B)) (sin B)))
310.0ms	(cbrt (/ (* x (cos B)) (sin B)))
343.0ms	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))

simplify104.0ms

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	131	50708