Details

sample180.0ms

Algorithm

intervals

Results

65.0ms	53×	body	640	valid
39.0ms	55×	body	1280	valid
17.0ms	154×	body	80	valid
6.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

34.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
21.0ms	(* x (/ 1.0 (tan B)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
28.0ms	(/ 1.0 (sin B))
51.0ms	(/ 1.0 (tan B))
194.0ms	(* x (/ 1.0 (tan B)))

simplify2.8s

Counts

129 → 129

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	188	1244
1	433	1180
2	1188	1075
3	3683	1067
done	5001	1067

prune602.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (pow (/ x (/ (tan B) 1.0)) 1)) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ x (/ (tan B) 1.0))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
130×	`*-un-lft-identity`
126×	`add-sqr-sqrt` `add-cube-cbrt`
100×	`fma-def`
88×	`unpow-prod-down`
49×	`distribute-rgt-neg-in`
48×	`distribute-lft-neg-in`
16×	`associate-/r*`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

3 → 218

Calls

3 calls:

417.0ms	(+ (- (pow (/ x (/ (tan B) 1.0)) 1)) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
9.0ms	(/ x (/ (tan B) 1.0))

series425.0ms

Counts

3 → 9

Calls

3 calls:

191.0ms	(+ (- (pow (/ x (/ (tan B) 1.0)) 1)) (/ 1.0 (sin B)))
36.0ms	(/ 1.0 (sin B))
197.0ms	(/ x (/ (tan B) 1.0))

simplify1.5s

Counts

227 → 227

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	243	1688
1	536	1537
2	1605	1427
done	5000	1425

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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))

rewrite163.0ms

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:

78.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
25.0ms	(* x (cos B))
13.0ms	(/ 1 (sin B))
26.0ms	(/ (* x (cos B)) (sin B))

series415.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
55.0ms	(* x (cos B))
35.0ms	(/ 1 (sin B))
167.0ms	(/ (* x (cos B)) (sin B))

simplify2.0s

Counts

216 → 216

Iterations

Useful iterations: done (2.0s)

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

prune580.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(/ (- (cos B)) (sin B))
0.5b	(cbrt (/ 1 (sin B)))
0.7b	(pow (cbrt (/ 1 (sin B))) 3)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
59×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`cbrt-prod`
16×	`unpow-prod-down` `cube-prod`
13×	`associate-/l*`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/r*`
5×	`div-inv`
4×	`expm1-log1p-u` `neg-mul-1` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `div-exp`
2×	`cbrt-undiv` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num`
1×	`cube-div` `neg-sub0` `cube-mult` `pow-to-exp` `rec-exp` `pow-flip` `1-exp` `unpow3` `div-sub` `distribute-frac-neg` `pow-exp` `inv-pow` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 169

Calls

4 calls:

23.0ms	(/ 1 (sin B))
19.0ms	(/ (- (cos B)) (sin B))
6.0ms	(cbrt (/ 1 (sin B)))
9.0ms	(pow (cbrt (/ 1 (sin B))) 3)

series454.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 1 (sin B))
58.0ms	(/ (- (cos B)) (sin B))
186.0ms	(cbrt (/ 1 (sin B)))
191.0ms	(pow (cbrt (/ 1 (sin B))) 3)

simplify1.4s

Counts

181 → 181

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	234	2043
1	513	1606
2	1336	1499
done	5000	1498

prune724.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
done	15	14

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.2s	1706×	body	1280	valid
1.9s	1451×	body	640	valid
1.2s	4938×	body	80	valid
464.0ms	726×	body	320	valid
158.0ms	334×	body	160	valid