Details

sample209.0ms

Algorithm

intervals

Results

75.0ms	61×	body	1280	valid
55.0ms	148×	body	80	valid
54.0ms	58×	body	640	valid
10.0ms	14×	body	320	valid
3.0ms	9×	body	160	valid

simplify115.0ms

Counts: 1 → 1

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

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

21.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ 1 (sin B))
5.0ms	(/ x (tan B))

series291.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

147.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
130.0ms	(/ x (tan B))
14.0ms	(/ 1 (sin B))

simplify645.0ms

Counts: 93 → 93

prune865.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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:

Slowest

21.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(/ (* x (cos B)) (sin B))
7.0ms	(* x (cos B))
5.0ms	(/ 1 (sin B))

series311.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(/ (* x (cos B)) (sin B))
112.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
52.0ms	(* x (cos B))
25.0ms	(/ 1 (sin B))

simplify2.4s

Counts: 108 → 108

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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×	`insert-posit16` `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 → 50

Calls

2 calls:

Slowest

15.0ms	(* x (cos B))
13.0ms	(/ (- 1 (* x (cos B))) (sin B))

series129.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

78.0ms	(/ (- 1 (* x (cos B))) (sin B))
51.0ms	(* x (cos B))

simplify3.0s

Counts: 56 → 56

prune506.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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)))

rewrite38.0ms

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

18.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms	(/ 1 (/ (tan B) x))
6.0ms	(/ 1 (sin B))
5.0ms	(/ (tan B) x)

series399.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

163.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
127.0ms	(/ 1 (/ (tan B) x))
83.0ms	(/ (tan B) x)
26.0ms	(/ 1 (sin B))

simplify662.0ms

Counts: 186 → 186

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes100.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.1s	1686×	body	1280	valid
1.8s	1483×	body	640	valid
1.7s	4864×	body	80	valid
719.0ms	733×	body	320	valid
207.0ms	352×	body	160	valid