Details

sample194.0ms

Algorithm

intervals

Results

61.0ms	20×	body	320	valid
27.0ms	38×	body	1280	valid
24.0ms	188×	body	80	valid
22.0ms	43×	body	640	valid
3.0ms	12×	body	160	valid

simplify109.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	59	11
6	61	11
done	61	11

prune77.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

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))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-r`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
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 → 135

Calls

4 calls:

57.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
7.0ms	(/ 1.0 (sin B))
8.0ms	(/ 1.0 (tan B))
91.0ms	(* x (/ 1.0 (tan B)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
23.0ms	(/ 1.0 (sin B))
52.0ms	(/ 1.0 (tan B))
203.0ms	(* x (/ 1.0 (tan B)))

simplify2.6s

Counts

147 → 147

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	199	1713
1	446	1635
2	1139	1489
3	3298	1451
done	5000	1440

prune633.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))

rewrite100.0ms

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×	`fma-neg` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 204

Calls

4 calls:

51.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
18.0ms	(* x (cos B))
8.0ms	(/ 1 (sin B))
13.0ms	(/ (* x (cos B)) (sin B))

series410.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
73.0ms	(* x (cos B))
16.0ms	(/ 1 (sin B))
166.0ms	(/ (* x (cos B)) (sin B))

simplify1.7s

Counts

216 → 216

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	264	6388
1	574	4918
2	1409	3868
done	5001	3101

prune460.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1 (/ 1 (sin B)) (* x (- (/ (cos B) (sin B)))))
0.1b	(/ 1 (sin B))
0.1b	(/ (cos B) (sin B))
0.3b	(* x (- (/ (cos B) (sin B))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
30×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`div-exp` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `clear-num`
1×	`neg-mul-1` `rec-exp` `pow-flip` `1-exp` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `fma-udef` `distribute-neg-frac` `inv-pow` `unswap-sqr`

Counts

4 → 121

Calls

4 calls:

0.0ms	(fma 1 (/ 1 (sin B)) (* x (- (/ (cos B) (sin B)))))
20.0ms	(/ 1 (sin B))
15.0ms	(/ (cos B) (sin B))
28.0ms	(* x (- (/ (cos B) (sin B))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(fma 1 (/ 1 (sin B)) (* x (- (/ (cos B) (sin B)))))
21.0ms	(/ 1 (sin B))
30.0ms	(/ (cos B) (sin B))
123.0ms	(* x (- (/ (cos B) (sin B))))

simplify2.6s

Counts

133 → 133

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	192	1322
1	382	1196
2	970	1112
3	3307	1112
done	5000	1111

prune552.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
16×	`associate-l`
12×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
4×	`div-exp` `unswap-sqr`
3×	`expm1-log1p-u` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `flip3--` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-*l/` `clear-num` `inv-pow`

Counts

3 → 104

Calls

3 calls:

17.0ms	(* x (cos B))
6.0ms	(/ 1 (sin B))
59.0ms	(* (/ 1 (sin B)) (- 1 (* x (cos B))))

series194.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* x (cos B))
28.0ms	(/ 1 (sin B))
114.0ms	(* (/ 1 (sin B)) (- 1 (* x (cos B))))

simplify5.1s

Counts

113 → 113

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	167	1333
1	378	1123
2	954	990
3	3239	984
done	5000	984

prune324.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	23	25
2	30	25
3	31	25
done	31	25

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.3s	1697×	body	1280	valid
1.3s	1431×	body	640	valid
1.1s	4914×	body	80	valid
566.0ms	342×	body	160	valid
371.0ms	709×	body	320	valid