Details

sample316.0ms

Algorithm

intervals

Results

139.0ms	60×	body	1280	valid
41.0ms	47×	body	640	valid
30.0ms	138×	body	80	valid
18.0ms	28×	body	320	valid
6.0ms	13×	body	160	valid

simplify115.0ms

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

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:

39.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (tan B))
42.0ms	(* x (/ 1.0 (tan B)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
25.0ms	(/ 1.0 (sin B))
62.0ms	(/ 1.0 (tan B))
221.0ms	(* x (/ 1.0 (tan B)))

simplify3.0s

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

prune581.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite536.0ms

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:

474.0ms	(+ (- (pow (/ x (/ (tan B) 1.0)) 1)) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
15.0ms	(/ x (/ (tan B) 1.0))

series387.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(+ (- (pow (/ x (/ (tan B) 1.0)) 1)) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (sin B))
151.0ms	(/ x (/ (tan B) 1.0))

simplify1.5s

Counts

227 → 227

Iterations

Useful iterations: done (1.4s)

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

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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)))
10.0ms	(* x (cos B))
6.0ms	(/ 1.0 (sin B))
19.0ms	(/ (* x (cos B)) (sin B))

series397.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
68.0ms	(* x (cos B))
28.0ms	(/ 1.0 (sin B))
118.0ms	(/ (* x (cos B)) (sin B))

simplify4.1s

Counts

108 → 108

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	162	1113
1	374	1066
2	1105	948
3	4914	937
done	5000	937

prune475.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `associate-/r*`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `associate-/r/` `fma-udef` `inv-pow`

Counts

3 → 117

Calls

3 calls:

0.0ms	(fma (pow x 1) (- (pow (/ 1 (/ (tan B) 1.0)) 1)) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
11.0ms	(/ 1 (/ (tan B) 1.0))

series270.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(fma (pow x 1) (- (pow (/ 1 (/ (tan B) 1.0)) 1)) (/ 1.0 (sin B)))
39.0ms	(/ 1.0 (sin B))
52.0ms	(/ 1 (/ (tan B) 1.0))

simplify2.7s

Counts

126 → 126

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	225	1588
1	461	1314
2	978	1111
3	2317	1093
done	5000	1085

prune445.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify11.0ms

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

sample6.4s

Algorithm

intervals

Results

2.3s	1713×	body	1280	valid
1.5s	1334×	body	640	valid
1.5s	4910×	body	80	valid
561.0ms	790×	body	320	valid
192.0ms	383×	body	160	valid