Details

sample78.0ms

Algorithm

intervals

Results

31.0ms	55×	body	1280	valid
15.0ms	45×	body	640	valid
13.0ms	165×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	30	11
3	40	11
4	51	11
5	54	11
done	54	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
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` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

10.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
10.0ms	(* x (/ 1.0 (tan B)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
40.0ms	(/ 1.0 (tan B))
113.0ms	(* x (/ 1.0 (tan B)))

simplify1.7s

Counts

115 → 115

Iterations

Useful iterations: 3 (844.0ms)

Iter	Nodes	Cost
0	180	1184
1	419	1125
2	1075	1022
3	3577	1017
done	5000	1017

prune311.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

30.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series240.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
108.0ms	(/ (* x 1.0) (tan B))

simplify1.9s

Counts

74 → 74

Iterations

Useful iterations: 3 (916.0ms)

Iter	Nodes	Cost
0	144	837
1	336	797
2	945	711
3	3838	706
done	5000	706

prune197.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))
0.1b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `distribute-lft-out`
3×	`rec-exp` `distribute-rgt-neg-in` `frac-2neg` `1-exp` `clear-num`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `pow-flip` `flip3-+` `neg-log` `frac-add` `associate-/r/` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 123

Calls

4 calls:

71.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(/ (tan B) (* x 1.0))
7.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
50.0ms	(/ (tan B) (* x 1.0))
86.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.0s

Counts

135 → 135

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	227	1699
1	533	1515
2	1364	1273
done	5000	1270

prune302.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

9.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series265.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
42.0ms	(* x (cos B))
99.0ms	(/ (* x (cos B)) (sin B))

simplify2.3s

Counts

94 → 94

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	154	1045
1	360	1002
2	1017	886
3	4768	879
done	5000	879

prune229.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.4s

Algorithm

intervals

Results

999.0ms	1700×	body	1280	valid
508.0ms	1461×	body	640	valid
397.0ms	4889×	body	80	valid
191.0ms	725×	body	320	valid
68.0ms	368×	body	160	valid