Details

sample216.0ms

Algorithm

intervals

Results

49.0ms	62×	body	1280	valid
19.0ms	42×	body	640	valid
19.0ms	169×	body	80	valid
7.0ms	22×	body	320	valid
3.0ms	11×	body	160	valid

simplify67.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	52	11
done	52	11

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

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)))

rewrite77.0ms

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:

35.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
22.0ms	(* x (/ 1.0 (tan B)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
25.0ms	(/ 1.0 (sin B))
44.0ms	(/ 1.0 (tan B))
185.0ms	(* x (/ 1.0 (tan B)))

simplify2.4s

Counts

115 → 115

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	180	1184
1	414	1125
2	1121	1022
3	3390	1017
done	5000	1017

prune516.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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))

rewrite119.0ms

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:

94.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
16.0ms	(/ (* x 1.0) (tan B))

series318.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
159.0ms	(/ (* x 1.0) (tan B))

simplify2.9s

Counts

74 → 74

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	144	837
1	334	797
2	988	711
3	3734	706
done	5000	706

prune360.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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`
3×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `associate-l` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

22.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
11.0ms	(/ x (sin B))
38.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

series449.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
30.0ms	(/ 1.0 (sin B))
70.0ms	(/ x (sin B))
162.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

simplify2.0s

Counts

102 → 102

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	173	1214
1	406	1164
2	1364	1019
done	5001	1012

prune383.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))))

rewrite97.0ms

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:

19.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
14.0ms	(/ (cos B) (sin B))
54.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
32.0ms	(/ 1.0 (sin B))
27.0ms	(/ (cos B) (sin B))
161.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	174	1253
1	405	1205
2	1272	1056
done	5000	1049

prune394.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	26	15
3	28	15
done	28	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1746×	body	1280	valid
767.0ms	1395×	body	640	valid
580.0ms	4973×	body	80	valid
272.0ms	743×	body	320	valid
85.0ms	348×	body	160	valid