Details

sample243.0ms

Algorithm

intervals

Results

64.0ms	17×	body	320	valid
61.0ms	62×	body	1280	valid
27.0ms	42×	body	640	valid
22.0ms	155×	body	80	valid
2.0ms	9×	body	160	valid

simplify65.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

70.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
11.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (tan B))
41.0ms	(* x (/ 1.0 (tan B)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
32.0ms	(/ 1.0 (sin B))
53.0ms	(/ 1.0 (tan B))
197.0ms	(* x (/ 1.0 (tan B)))

simplify691.0ms

Counts: 113 → 113

prune467.0ms

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `div-inv` `difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

67.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
8.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series353.0ms

Counts

3 → 9

Calls

3 calls:

184.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
37.0ms	(/ 1.0 (sin B))
132.0ms	(/ (* x 1.0) (tan B))

simplify577.0ms

Counts: 74 → 74

prune227.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
0.1b	(/ 1.0 (sin B))
0.2b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

24.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
11.0ms	(/ 1.0 (sin B))
26.0ms	(* x (cos B))
26.0ms	(/ (* x (cos B)) (sin B))

series435.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
37.0ms	(/ 1.0 (sin B))
72.0ms	(* x (cos B))
129.0ms	(/ (* x (cos B)) (sin B))

simplify657.0ms

Counts: 93 → 93

prune335.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

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)))

rewrite57.0ms

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:

28.0ms	(* (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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

393.0ms	(* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B))))
241.0ms	(cbrt (/ (* x (cos B)) (sin B)))
224.0ms	(cbrt (/ (* x (cos B)) (sin B)))
270.0ms	(cbrt (/ (* x (cos B)) (sin B)))

simplify1.9s

Counts: 115 → 115

prune661.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

-27.4% (0.2b remaining)

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

bsearch0.0ms

simplify1.7s

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.6s	1793×	body	1280	valid
1.9s	4906×	body	80	valid
1.2s	1386×	body	640	valid
492.0ms	729×	body	320	valid
118.0ms	346×	body	160	valid