Details

sample569.0ms

Algorithm

intervals

Results

163.0ms	49×	body	640	valid
117.0ms	57×	body	1280	valid
55.0ms	156×	body	80	valid
20.0ms	21×	body	320	valid
8.0ms	11×	body	160	valid

simplify200.0ms

Counts: 1 → 1

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 3 expressions with local error:

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

rewrite236.0ms

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:

Slowest

203.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
10.0ms	(/ x (tan B))
7.0ms	(/ 1 (sin B))

series372.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

178.0ms	(/ x (tan B))
167.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
26.0ms	(/ 1 (sin B))

simplify563.0ms

Counts: 93 → 93

prune904.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

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-l`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`div-exp` `insert-posit16`
3×	`cbrt-undiv` `associate-r` `associate-*l/` `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:

Slowest

24.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
20.0ms	(* (/ x (sin B)) (cos B))
11.0ms	(/ 1 (sin B))
9.0ms	(/ x (sin B))

series405.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

170.0ms	(* (/ x (sin B)) (cos B))
147.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
57.0ms	(/ x (sin B))
30.0ms	(/ 1 (sin B))

simplify1.5s

Counts: 120 → 120

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (tan B) x))
0.2b	(/ (tan B) x)
0.1b	(/ 1 (sin B))
0.0b	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

Slowest

26.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms	(/ 1 (/ (tan B) x))
6.0ms	(/ (tan B) x)
5.0ms	(/ 1 (sin B))

series324.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
116.0ms	(/ 1 (/ (tan B) x))
70.0ms	(/ (tan B) x)
14.0ms	(/ 1 (sin B))

simplify751.0ms

Counts: 186 → 186

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

8.7b	(/ (- (/ (tan B) x) (sin B)) (* (sin B) (/ (tan B) x)))
0.2b	(* (sin B) (/ (tan B) x))
0.2b	(/ (tan B) x)
0.2b	(/ (tan B) x)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
36×	`times-frac`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r`
12×	`associate-/l*`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `div-inv` `add-log-exp` `difference-of-squares` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-l`
2×	`tan-quot` `associate-*r/` `distribute-lft-out--` `unswap-sqr`
1×	`flip3--` `div-sub` `pow-prod-down` `associate-/r/` `*-commutative` `flip--`

Counts

4 → 125

Calls

4 calls:

Slowest

45.0ms	(/ (- (/ (tan B) x) (sin B)) (* (sin B) (/ (tan B) x)))
13.0ms	(* (sin B) (/ (tan B) x))
6.0ms	(/ (tan B) x)
6.0ms	(/ (tan B) x)

series509.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

272.0ms	(/ (- (/ (tan B) x) (sin B)) (* (sin B) (/ (tan B) x)))
107.0ms	(* (sin B) (/ (tan B) x))
65.0ms	(/ (tan B) x)
64.0ms	(/ (tan B) x)

simplify613.0ms

Counts: 137 → 137

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes141.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.7s	1769×	body	1280	valid
2.1s	1369×	body	640	valid
2.0s	4874×	body	80	valid
723.0ms	747×	body	320	valid
220.0ms	353×	body	160	valid