Details

sample423.0ms

Algorithm

intervals

Results

60.0ms	62×	body	1280	valid
15.0ms	42×	body	640	valid
13.0ms	169×	body	80	valid
5.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6
done	53	6

prune7.0ms

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)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite57.0ms

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:

22.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
19.0ms	(* x (/ 1.0 (tan B)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
37.0ms	(/ 1.0 (tan B))
126.0ms	(* x (/ 1.0 (tan B)))

simplify50.0ms

Counts

115 → 115

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	419	664
1	1645	609
2	5001	604
done	5001	604

prune300.0ms

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)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (tan B))

rewrite68.0ms

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:

48.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series248.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
112.0ms	(/ (* x 1.0) (tan B))

simplify37.0ms

Counts

74 → 74

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	336	465
1	1303	419
2	5001	414
done	5001	414

prune194.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

18.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ (cos B) (sin B))
24.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
20.0ms	(/ (cos B) (sin B))
105.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

simplify48.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	410	735
1	1582	648
2	5001	642
done	5001	642

prune257.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 107

Calls

4 calls:

5.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (sin B))
32.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
15.0ms	(* x (/ 1.0 (sin B)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (sin B))
106.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
55.0ms	(* x (/ 1.0 (sin B)))

simplify47.0ms

Counts

119 → 119

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	315	645
1	1562	560
2	5001	560
done	5001	560

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	25	9
2	27	9
3	27	9
done	27	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1746×	body	1280	valid
496.0ms	1395×	body	640	valid
392.0ms	4973×	body	80	valid
189.0ms	743×	body	320	valid
59.0ms	348×	body	160	valid