Details

sample408.0ms

Algorithm

intervals

Results

53.0ms	54×	body	1280	valid
18.0ms	47×	body	640	valid
15.0ms	150×	body	80	valid
7.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6
done	62	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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:

22.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (tan B))
5.0ms	(/ 1.0 (sin B))
20.0ms	(* x (/ 1.0 (tan B)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
39.0ms	(/ 1.0 (tan B))
20.0ms	(/ 1.0 (sin B))
127.0ms	(* x (/ 1.0 (tan B)))

simplify51.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	438	696
1	1724	639
2	5002	635
done	5002	635

prune367.0ms

Pruning

9 alts after pruning (9 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)))
0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ 1.0 (sin B))

rewrite78.0ms

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:

56.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
13.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ 1.0 (sin B))

series275.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
113.0ms	(/ (* x 1.0) (tan B))
20.0ms	(/ 1.0 (sin B))

simplify47.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	350	492
1	1353	445
2	5001	440
done	5001	440

prune283.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`prod-exp` `cbrt-unprod` `fma-udef`

Counts

3 → 62

Calls

3 calls:

0.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))
13.0ms	(/ (* x 1.0) (sin B))
6.0ms	(/ 1.0 (sin B))

series178.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))
56.0ms	(/ (* x 1.0) (sin B))
20.0ms	(/ 1.0 (sin B))

simplify116.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	259	414
1	1045	365
2	4584	365
3	5002	364
done	5002	364

prune211.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (/ 1 (/ (sin B) (* x 1.0)))) (cos B) (/ 1.0 (sin B)))
0.1b	(/ (sin B) (* x 1.0))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1 (/ (sin B) (* x 1.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
32×	`add-exp-log`
30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv`
7×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
2×	`cbrt-unprod`
1×	`pow-flip` `associate-/r/` `fma-udef` `inv-pow`

Counts

4 → 120

Calls

4 calls:

0.0ms	(fma (- (/ 1 (/ (sin B) (* x 1.0)))) (cos B) (/ 1.0 (sin B)))
12.0ms	(/ (sin B) (* x 1.0))
6.0ms	(/ 1.0 (sin B))
17.0ms	(/ 1 (/ (sin B) (* x 1.0)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(fma (- (/ 1 (/ (sin B) (* x 1.0)))) (cos B) (/ 1.0 (sin B)))
36.0ms	(/ (sin B) (* x 1.0))
19.0ms	(/ 1.0 (sin B))
54.0ms	(/ 1 (/ (sin B) (* x 1.0)))

simplify47.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	451	849
1	1931	733
2	5002	688
done	5002	688

prune303.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

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: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	19	8
2	19	8
done	19	8

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	1729×	body	1280	valid
517.0ms	1388×	body	640	valid
425.0ms	4942×	body	80	valid
188.0ms	686×	body	320	valid
68.0ms	391×	body	160	valid