Details

sample531.0ms

Algorithm

intervals

Results

104.0ms	16×	body	160	valid
87.0ms	50×	body	1280	valid
76.0ms	153×	body	80	valid
65.0ms	27×	body	320	valid
61.0ms	45×	body	640	valid

simplify250.0ms

Counts: 1 → 1

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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

39.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms	(/ x (tan B))
6.0ms	(/ 1 (sin B))

series411.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

222.0ms	(/ x (tan B))
161.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
28.0ms	(/ 1 (sin B))

simplify824.0ms

Counts: 294 → 294

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite83.0ms

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

29.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
23.0ms	(/ (* x (cos B)) (sin B))
15.0ms	(* x (cos B))
10.0ms	(/ 1 (sin B))

series374.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(/ (* x (cos B)) (sin B))
131.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
60.0ms	(* x (cos B))
26.0ms	(/ 1 (sin B))

simplify736.0ms

Counts: 220 → 220

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
36×	`add-exp-log`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube`
16×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`pow1` `cbrt-undiv`
7×	`div-inv`
5×	`prod-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l` `cbrt-unprod`
2×	`pow-flip` `inv-pow`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

Slowest

20.0ms	(* x (cos B))
18.0ms	(/ 1 (/ (sin B) (* x (cos B))))
12.0ms	(/ (sin B) (* x (cos B)))
10.0ms	(/ 1 (sin B))

series235.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

104.0ms	(/ 1 (/ (sin B) (* x (cos B))))
71.0ms	(/ (sin B) (* x (cos B)))
46.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))

simplify2.5s

Counts: 150 → 150

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

11.5b	(/ (- (tan B) (* (sin B) x)) (* (sin B) (tan B)))
0.1b	(* (sin B) (tan B))
0.1b	(* (sin B) x)
0.0b	(- (tan B) (* (sin B) x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

Slowest

52.0ms	(/ (- (tan B) (* (sin B) x)) (* (sin B) (tan B)))
24.0ms	(* (sin B) (tan B))
22.0ms	(- (tan B) (* (sin B) x))
17.0ms	(* (sin B) x)

series525.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

258.0ms	(/ (- (tan B) (* (sin B) x)) (* (sin B) (tan B)))
124.0ms	(- (tan B) (* (sin B) x))
83.0ms	(* (sin B) (tan B))
60.0ms	(* (sin B) x)

simplify3.2s

Counts: 104 → 104

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample9.3s

Algorithm

intervals

Results

4.0s	1784×	body	1280	valid
2.1s	4931×	body	80	valid
2.1s	1407×	body	640	valid
636.0ms	720×	body	320	valid
226.0ms	348×	body	160	valid