Details

sample255.0ms

Algorithm

intervals

Results

94.0ms	65×	body	1280	valid
63.0ms	46×	body	640	valid
41.0ms	19×	body	320	valid
34.0ms	145×	body	80	valid
9.0ms	16×	body	160	valid

simplify114.0ms

Counts: 1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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)))

rewrite62.0ms

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:

Slowest

31.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms	(/ 1 (sin B))
6.0ms	(/ x (tan B))

series302.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

148.0ms	(/ x (tan B))
133.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
22.0ms	(/ 1 (sin B))

simplify709.0ms

Counts: 294 → 294

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:

Slowest

24.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
19.0ms	(/ (* x (cos B)) (sin B))
13.0ms	(* x (cos B))
8.0ms	(/ 1 (sin B))

series319.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

142.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
113.0ms	(/ (* x (cos B)) (sin B))
43.0ms	(* x (cos B))
22.0ms	(/ 1 (sin B))

simplify700.0ms

Counts: 220 → 220

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

2 → 54

Calls

2 calls:

Slowest

22.0ms	(/ (- 1 (* x (cos B))) (sin B))
13.0ms	(* x (cos B))

series171.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

99.0ms	(/ (- 1 (* x (cos B))) (sin B))
72.0ms	(* x (cos B))

simplify749.0ms

Counts: 60 → 60

prune642.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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:

Slowest

25.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
15.0ms	(* x (/ (cos B) (sin B)))
9.0ms	(/ (cos B) (sin B))
5.0ms	(/ 1 (sin B))

series283.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(* x (/ (cos B) (sin B)))
116.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
30.0ms	(/ (cos B) (sin B))
16.0ms	(/ 1 (sin B))

simplify2.1s

Counts: 154 → 154

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes182.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample9.1s

Algorithm

intervals

Results

3.7s	1672×	body	1280	valid
2.4s	4983×	body	80	valid
1.9s	1410×	body	640	valid
624.0ms	720×	body	320	valid
211.0ms	370×	body	160	valid