Details

sample295.0ms

Algorithm

intervals

Results

76.0ms	57×	body	1280	valid
36.0ms	42×	body	640	valid
36.0ms	168×	body	80	valid
15.0ms	23×	body	320	valid
4.0ms	9×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
29	4790
28	4572
27	4388
26	4180
25	3967
24	3753
23	3564
22	3407
21	3205
20	3006
19	2833
18	2631
17	2458
16	2289
15	2130
14	1959
13	1787
12	1570
11	1347
10	1172
9	1050
8	909
7	752
6	541
5	310
4	185
3	85
2	45
1	20
0	10

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
215×	`add-cube-cbrt`
182×	`prod-diff`
31×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 285

Calls

3 calls:

55.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
9.0ms	(/ 1 (sin B))
17.0ms	(/ x (tan B))

series323.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
19.0ms	(/ 1 (sin B))
162.0ms	(/ x (tan B))

simplify1.6s

Counts

294 → 294

Iterations

Iter	Nodes
done	5001
2	1990
1	848
0	381

prune999.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`add-cbrt-cube` `fma-neg`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `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 → 208

Calls

4 calls:

59.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
18.0ms	(* x (cos B))
17.0ms	(/ 1 (sin B))
19.0ms	(/ (* x (cos B)) (sin B))

series330.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
47.0ms	(* x (cos B))
15.0ms	(/ 1 (sin B))
144.0ms	(/ (* x (cos B)) (sin B))

simplify2.3s

Counts

220 → 220

Iterations

Iter	Nodes
done	5001
2	1634
1	613
0	269

prune828.0ms

Pruning

7 alts after pruning (7 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)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-exp-log`
13×	`add-cbrt-cube` `fma-neg` `associate-r` `prod-diff`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-l` `associate-*r/`
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 → 142

Calls

4 calls:

62.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
12.0ms	(/ 1 (sin B))
20.0ms	(/ (cos B) (sin B))
32.0ms	(* x (/ (cos B) (sin B)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
25.0ms	(/ 1 (sin B))
25.0ms	(/ (cos B) (sin B))
135.0ms	(* x (/ (cos B) (sin B)))

simplify1.6s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	1498
1	436
0	192

prune570.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize40.0ms

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)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
16×	`associate-l`
12×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
4×	`div-exp` `unswap-sqr`
3×	`expm1-log1p-u` `associate-/r` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `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 → 107

Calls

3 calls:

18.0ms	(* (cos B) x)
13.0ms	(/ 1 (sin B))
59.0ms	(* (/ 1 (sin B)) (- 1 (* (cos B) x)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (cos B) x)
26.0ms	(/ 1 (sin B))
95.0ms	(* (/ 1 (sin B)) (- 1 (* (cos B) x)))

simplify3.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5004
3	2944
2	1083
1	454
0	177

prune480.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes106.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	1772×	body	1280	valid
1.7s	1405×	body	640	valid
1.5s	4963×	body	80	valid
705.0ms	702×	body	320	valid
177.0ms	353×	body	160	valid