Details

sample116.0ms

Algorithm

intervals

Results

46.0ms	58×	body	1280	valid
22.0ms	40×	body	640	valid
21.0ms	166×	body	80	valid
6.0ms	16×	body	320	valid
5.0ms	17×	body	160	valid

simplify4.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

25.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
9.0ms	(/ 1.0 (tan B))
64.0ms	(* x (/ 1.0 (tan B)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
32.0ms	(/ 1.0 (sin B))
60.0ms	(/ 1.0 (tan B))
162.0ms	(* x (/ 1.0 (tan B)))

simplify43.0ms

Counts: 115 → 115

prune411.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log` `times-frac`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

44.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
13.0ms	(* x (cos B))
13.0ms	(/ 1 (sin B))
12.0ms	(/ (* x (cos B)) (sin B))

series315.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
40.0ms	(* x (cos B))
25.0ms	(/ 1 (sin B))
132.0ms	(/ (* x (cos B)) (sin B))

simplify43.0ms

Counts: 104 → 104

prune248.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan B)) (cbrt (tan B)))
0.5b	(cbrt (tan B))
0.5b	(cbrt (tan B))
0.5b	(cbrt (tan B))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

22.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))

series641.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
152.0ms	(cbrt (tan B))
147.0ms	(cbrt (tan B))
144.0ms	(cbrt (tan B))

simplify63.0ms

Counts: 91 → 91

prune320.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
31.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series743.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt (/ 1.0 (sin B)))
179.0ms	(cbrt (/ 1.0 (sin B)))
179.0ms	(cbrt (/ 1.0 (sin B)))
193.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify82.0ms

Counts: 156 → 156

prune624.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes98.0ms

Accuracy

-41.1% (0.2b remaining)

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

bsearch0.0ms

simplify367.0ms

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.7s	1730×	body	1280	valid
1.1s	1449×	body	640	valid
976.0ms	4913×	body	80	valid
326.0ms	705×	body	320	valid
142.0ms	339×	body	160	valid