Details

sample403.0ms

Algorithm

intervals

Results

178.0ms	60×	body	1280	valid
68.0ms	47×	body	640	valid
30.0ms	138×	body	80	valid
15.0ms	28×	body	320	valid
5.0ms	13×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	52	11
done	52	11

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

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))
0.3b	(* x (/ 1.0 (tan B)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `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:

64.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
11.0ms	(/ 1.0 (sin B))
9.0ms	(/ 1.0 (tan B))
25.0ms	(* x (/ 1.0 (tan B)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
34.0ms	(/ 1.0 (sin B))
72.0ms	(/ 1.0 (tan B))
241.0ms	(* x (/ 1.0 (tan B)))

simplify2.3s

Counts

113 → 113

Iterations

Useful iterations: 2 (295.0ms)

Iter	Nodes	Cost
0	174	1141
1	383	1074
2	964	996
3	2656	996
done	5000	996

prune460.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-r` `pow-prod-down` `associate-l/`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `*-commutative` `frac-sub` `flip--` `sub-div`

Counts

4 → 89

Calls

4 calls:

61.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
11.0ms	(/ x (sin B))
6.0ms	(/ 1.0 (sin B))
45.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

series452.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
88.0ms	(/ x (sin B))
42.0ms	(/ 1.0 (sin B))
152.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

simplify2.1s

Counts

101 → 101

Iterations

Useful iterations: 2 (263.0ms)

Iter	Nodes	Cost
0	168	1176
1	378	1109
2	1208	996
done	5000	996

prune391.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
7×	`pow1`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `flip--` `div-inv`

Counts

2 → 48

Calls

2 calls:

30.0ms	(* (* 1.0 x) (cos B))
21.0ms	(/ (- 1.0 (* (* 1.0 x) (cos B))) (sin B))

series192.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(* (* 1.0 x) (cos B))
113.0ms	(/ (- 1.0 (* (* 1.0 x) (cos B))) (sin B))

simplify2.6s

Counts

54 → 54

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	108	789
1	254	764
2	853	676
3	3235	674
done	5000	674

prune237.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* 1.0 x) (cos B))
0.1b	(/ (sin B) (- 1.0 (* (* 1.0 x) (cos B))))
0.2b	(/ 1 (/ (sin B) (- 1.0 (* (* 1.0 x) (cos B)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
18×	`associate-/r*`
15×	`add-cbrt-cube`
11×	`associate-/r/`
9×	`pow1`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `associate-l` `*-commutative` `inv-pow`

Counts

3 → 131

Calls

3 calls:

19.0ms	(* (* 1.0 x) (cos B))
15.0ms	(/ (sin B) (- 1.0 (* (* 1.0 x) (cos B))))
16.0ms	(/ 1 (/ (sin B) (- 1.0 (* (* 1.0 x) (cos B)))))

series349.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(* (* 1.0 x) (cos B))
123.0ms	(/ (sin B) (- 1.0 (* (* 1.0 x) (cos B))))
142.0ms	(/ 1 (/ (sin B) (- 1.0 (* (* 1.0 x) (cos B)))))

simplify1.6s

Counts

140 → 140

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	244	2965
1	555	2672
2	1534	2433
done	5000	2379

prune420.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes150.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	15	13
done	15	13

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.7s	1713×	body	1280	valid
1.6s	1334×	body	640	valid
1.3s	4910×	body	80	valid
375.0ms	790×	body	320	valid
125.0ms	383×	body	160	valid