Details

sample412.0ms

Algorithm

intervals

Results

50.0ms	51×	body	1280	valid
17.0ms	51×	body	640	valid
12.0ms	157×	body	80	valid
6.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify56.0ms

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

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

rewrite50.0ms

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:

15.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
19.0ms	(* x (/ 1.0 (tan B)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
37.0ms	(/ 1.0 (tan B))
131.0ms	(* x (/ 1.0 (tan B)))

simplify1.7s

Counts

129 → 129

Iterations

Useful iterations: 3 (822.0ms)

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

prune362.0ms

Pruning

11 alts after pruning (11 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))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

52.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
8.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series256.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
115.0ms	(/ (* x 1.0) (tan B))

simplify1.8s

Counts

100 → 100

Iterations

Useful iterations: 3 (855.0ms)

Iter	Nodes	Cost
0	150	887
1	348	843
2	1039	755
3	3938	747
done	5000	747

prune272.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

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:

37.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
6.0ms	(/ 1 (sin B))
8.0ms	(* x (cos B))
12.0ms	(/ (* x (cos B)) (sin B))

series251.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
14.0ms	(/ 1 (sin B))
40.0ms	(* x (cos B))
100.0ms	(/ (* x (cos B)) (sin B))

simplify1.2s

Counts

216 → 216

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	264	6388
1	574	4918
2	1410	3868
done	5000	3101

prune330.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

107×	`times-frac`
68×	`*-un-lft-identity`
59×	`add-sqr-sqrt` `add-cube-cbrt`
56×	`fma-def`
32×	`add-exp-log`
29×	`distribute-rgt-neg-in`
26×	`distribute-lft-neg-in`
20×	`add-cbrt-cube`
16×	`div-inv`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/r/`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `pow-flip` `flip3-+` `neg-log` `frac-add` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 187

Calls

4 calls:

101.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
9.0ms	(/ (tan B) (* x 1.0))
17.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
54.0ms	(/ (tan B) (* x 1.0))
93.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.2s

Counts

199 → 199

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	235	1771
1	538	1578
2	1426	1329
done	5000	1322

prune470.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	15	11
done	15	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

997.0ms	1726×	body	1280	valid
482.0ms	1395×	body	640	valid
406.0ms	4997×	body	80	valid
183.0ms	715×	body	320	valid
59.0ms	354×	body	160	valid