Details

sample142.0ms

Algorithm

intervals

Results

52.0ms	62×	body	1280	valid
41.0ms	155×	body	80	valid
23.0ms	42×	body	640	valid
6.0ms	17×	body	320	valid
3.0ms	9×	body	160	valid

simplify39.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))
0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite55.0ms

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:

23.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
18.0ms	(* x (/ 1.0 (tan B)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
49.0ms	(/ 1.0 (tan B))
157.0ms	(* x (/ 1.0 (tan B)))

simplify690.0ms

Counts: 115 → 115

prune702.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

78.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series323.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
145.0ms	(/ (* x 1.0) (tan B))

simplify541.0ms

Counts: 74 → 74

prune298.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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:

32.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(/ 1 (sin B))
14.0ms	(* x (cos B))
27.0ms	(/ (* x (cos B)) (sin B))

series327.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
19.0ms	(/ 1 (sin B))
61.0ms	(* x (cos B))
130.0ms	(/ (* x (cos B)) (sin B))

simplify586.0ms

Counts: 104 → 104

prune409.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))
0.5b	(cbrt (/ (* x (cos B)) (sin B)))
0.5b	(cbrt (/ (* x (cos B)) (sin B)))
0.5b	(cbrt (/ (* x (cos B)) (sin B)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

53×	`cbrt-prod`
30×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
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 → 103

Calls

4 calls:

22.0ms	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))
8.0ms	(cbrt (/ (* x (cos B)) (sin B)))
8.0ms	(cbrt (/ (* x (cos B)) (sin B)))
8.0ms	(cbrt (/ (* x (cos B)) (sin B)))

series1.0s

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))
236.0ms	(cbrt (/ (* x (cos B)) (sin B)))
248.0ms	(cbrt (/ (* x (cos B)) (sin B)))
264.0ms	(cbrt (/ (* x (cos B)) (sin B)))

simplify1.9s

Counts: 115 → 115

prune626.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

-33.6% (0.2b remaining)

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

bsearch0.0ms

simplify1.4s

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	1793×	body	1280	valid
1.6s	1386×	body	640	valid
1.0s	4906×	body	80	valid
553.0ms	729×	body	320	valid
109.0ms	346×	body	160	valid