Details

sample471.0ms

Algorithm

intervals

Results

218.0ms	53×	body	1280	valid
32.0ms	38×	body	640	valid
31.0ms	147×	body	80	valid
18.0ms	28×	body	320	valid
7.0ms	17×	body	160	valid

simplify233.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (56.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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)))

rewrite108.0ms

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:

44.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
43.0ms	(* x (/ 1.0 (tan B)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
49.0ms	(/ 1.0 (sin B))
80.0ms	(/ 1.0 (tan B))
380.0ms	(* x (/ 1.0 (tan B)))

simplify2.7s

Counts

129 → 129

Iterations

Useful iterations: 3 (1.3s)

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

prune667.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
57×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`fma-def` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`distribute-rgt-neg-in` `frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `flip3-+` `associate-*r/` `neg-log` `frac-add` `associate-/r/` `flip-+` `distribute-neg-frac`

Counts

3 → 125

Calls

3 calls:

17.0ms	(+ (- (* 1 (/ x (/ (tan B) 1.0)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
9.0ms	(/ x (/ (tan B) 1.0))

series384.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(+ (- (* 1 (/ x (/ (tan B) 1.0)))) (/ 1.0 (sin B)))
27.0ms	(/ 1.0 (sin B))
174.0ms	(/ x (/ (tan B) 1.0))

simplify2.1s

Counts

134 → 134

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	251	1707
1	563	1555
2	1728	1455
done	5000	1446

prune686.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

19.0ms	(/ 1.0 (sin B))
1.0ms	(fma x (- (/ 1.0 (tan B))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (tan B))

series253.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1.0 (sin B))
187.0ms	(fma x (- (/ 1.0 (tan B))) (/ 1.0 (sin B)))
43.0ms	(/ 1.0 (tan B))

simplify3.1s

Counts

78 → 78

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	130	730
1	246	704
2	529	644
3	1098	644
4	2970	636
done	5000	636

prune405.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`distribute-rgt-neg-in` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

22.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (sin B))
18.0ms	(* x (cos B))
33.0ms	(/ (* x (cos B)) (sin B))

series347.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
42.0ms	(* x (cos B))
148.0ms	(/ (* x (cos B)) (sin B))

simplify3.7s

Counts

108 → 108

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	162	1113
1	374	1066
2	1109	948
3	4921	937
done	5000	937

prune368.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	22	15
3	28	15
done	28	15

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.2s	1654×	body	1280	valid
1.7s	1505×	body	640	valid
1.4s	4888×	body	80	valid
389.0ms	702×	body	320	valid
152.0ms	344×	body	160	valid