Details

sample216.0ms

Algorithm

intervals

Results

46.0ms	57×	body	1280	valid
43.0ms	20×	body	320	valid
27.0ms	48×	body	640	valid
21.0ms	155×	body	80	valid
2.0ms	7×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	53	11
done	53	11

prune658.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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:

23.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
5.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
28.0ms	(* x (/ 1.0 (tan B)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
25.0ms	(/ 1.0 (sin B))
42.0ms	(/ 1.0 (tan B))
138.0ms	(* x (/ 1.0 (tan B)))

simplify848.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (263.0ms)

Iter	Nodes	Cost
0	175	1141
1	410	1078
2	1459	996
done	5001	996

prune598.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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:

39.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
14.0ms	(* x (cos B))
9.0ms	(/ 1.0 (sin B))
20.0ms	(/ (* x (cos B)) (sin B))

series466.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
67.0ms	(* x (cos B))
41.0ms	(/ 1.0 (sin B))
139.0ms	(/ (* x (cos B)) (sin B))

simplify917.0ms

Counts

93 → 93

Iterations

Useful iterations: done (913.0ms)

Iter	Nodes	Cost
0	150	1006
1	355	964
2	1458	869
done	5001	863

prune448.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin B))
0.5b	(cbrt (sin B))
0.5b	(cbrt (sin B))
0.5b	(* (cbrt (sin B)) (cbrt (sin B)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
32.0ms	(* (cbrt (sin B)) (cbrt (sin B)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (sin B))
167.0ms	(cbrt (sin B))
136.0ms	(cbrt (sin B))
140.0ms	(* (cbrt (sin B)) (cbrt (sin B)))

simplify1.2s

Counts

85 → 85

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	75	710
1	177	628
2	695	534
done	5000	520

prune523.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
0.4b	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
0.4b	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
0.5b	(* (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))) (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-*r/`
11×	`pow1` `flip3--` `frac-sub` `flip--`
9×	`frac-times` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-*l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

19.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
21.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
21.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
152.0ms	(* (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))) (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))

series892.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
236.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
234.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
238.0ms	(* (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))) (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))

simplify797.0ms

Counts

109 → 109

Iterations

Useful iterations: done (793.0ms)

Iter	Nodes	Cost
0	201	3926
1	504	3710
2	2021	3491
done	5000	3258

prune679.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes189.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14
done	12	14

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.4s	1690×	body	1280	valid
1.4s	4996×	body	80	valid
1.1s	1437×	body	640	valid
309.0ms	710×	body	320	valid
240.0ms	377×	body	160	valid