Details

sample152.0ms

Algorithm

intervals

Results

56.0ms	168×	body	80	valid
46.0ms	57×	body	1280	valid
24.0ms	42×	body	640	valid
9.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
35	4970
34	4828
33	4665
32	4493
31	4330
30	4139
29	3972
28	3794
27	3608
26	3434
25	3297
24	3150
23	2978
22	2834
21	2632
20	2448
19	2290
18	2119
17	1964
16	1837
15	1728
14	1603
13	1490
12	1330
11	1186
10	1061
9	917
8	762
7	635
6	430
5	255
4	161
3	80
2	43
1	20
0	10

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ x (tan B)))
0.1b	(/ 1 (sin B))
0.1b	(/ x (tan B))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
19×	`add-cube-cbrt`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`div-exp` `insert-posit16` `div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 84

Calls

3 calls:

35.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
6.0ms	(/ 1 (sin B))
6.0ms	(/ x (tan B))

series316.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
23.0ms	(/ 1 (sin B))
133.0ms	(/ x (tan B))

simplify1.4s

Counts

93 → 93

Iterations

Iter	Nodes
done	5049
3	2697
2	849
1	300
0	153

prune303.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

39.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
15.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))
12.0ms	(/ (* x (cos B)) (sin B))

series280.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
43.0ms	(* x (cos B))
16.0ms	(/ 1 (sin B))
123.0ms	(/ (* x (cos B)) (sin B))

simplify1.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1063
1	329
0	150

prune430.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
0.1b	(/ 1 (sin B))
0.1b	(/ (cos B) (sin B))
0.3b	(* x (/ (cos B) (sin B)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
15×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`div-exp` `insert-posit16`
3×	`cbrt-undiv` `associate-l` `associate-*r/` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div`

Counts

4 → 108

Calls

4 calls:

35.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
6.0ms	(/ 1 (sin B))
9.0ms	(/ (cos B) (sin B))
20.0ms	(* x (/ (cos B) (sin B)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
25.0ms	(/ 1 (sin B))
34.0ms	(/ (cos B) (sin B))
105.0ms	(* x (/ (cos B) (sin B)))

simplify2.9s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
3	4635
2	1299
1	373
0	168

prune594.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
16×	`associate-l`
12×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-r`
5×	`prod-exp`
4×	`div-exp` `unswap-sqr`
3×	`associate-/r` `cbrt-unprod` `insert-posit16` `associate-/l` `add-log-exp`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `associate-*l/` `pow-flip` `inv-pow`

Counts

3 → 95

Calls

3 calls:

18.0ms	(* (cos B) x)
13.0ms	(/ 1 (sin B))
33.0ms	(* (/ 1 (sin B)) (- 1 (* (cos B) x)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (cos B) x)
15.0ms	(/ 1 (sin B))
81.0ms	(* (/ 1 (sin B)) (- 1 (* (cos B) x)))

simplify2.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
3	2882
2	1081
1	396
0	157

prune433.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.3s	1772×	body	1280	valid
1.6s	1405×	body	640	valid
957.0ms	4963×	body	80	valid
430.0ms	702×	body	320	valid
125.0ms	353×	body	160	valid