Details

sample125.0ms

Algorithm

intervals

Results

54.0ms	50×	body	1280	valid
24.0ms	50×	body	640	valid
20.0ms	160×	body	80	valid
9.0ms	25×	body	320	valid
2.0ms	7×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	53	11
done	53	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize341.0ms

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

rewrite64.0ms

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:

26.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
7.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
20.0ms	(* x (/ 1.0 (tan B)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
24.0ms	(/ 1.0 (sin B))
44.0ms	(/ 1.0 (tan B))
178.0ms	(* x (/ 1.0 (tan B)))

simplify910.0ms

Counts

115 → 115

Iterations

Useful iterations: done (905.0ms)

Iter	Nodes	Cost
0	180	1184
1	443	1129
2	1636	1030
done	5000	1023

prune443.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite112.0ms

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:

76.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
22.0ms	(/ (* x 1.0) (tan B))
7.0ms	(/ 1.0 (sin B))

series336.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
162.0ms	(/ (* x 1.0) (tan B))
29.0ms	(/ 1.0 (sin B))

simplify963.0ms

Counts

74 → 74

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	144	837
1	356	797
2	1504	717
done	5000	714

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))
0.2b	(/ (* x (cos B)) (sin B))

rewrite71.0ms

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:

25.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
13.0ms	(* x (cos B))
9.0ms	(/ 1.0 (sin B))
20.0ms	(/ (* x (cos B)) (sin B))

series332.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
38.0ms	(* x (cos B))
22.0ms	(/ 1.0 (sin B))
136.0ms	(/ (* x (cos B)) (sin B))

simplify1.0s

Counts

94 → 94

Iterations

Useful iterations: done (998.0ms)

Iter	Nodes	Cost
0	154	1045
1	379	1002
2	1552	892
done	5000	879

prune390.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

34.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
17.0ms	(/ (* x 1.0) (sin B))
40.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series346.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
66.0ms	(/ (* x 1.0) (sin B))
147.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	165	1259
1	447	1211
2	2325	1058
done	5000	1054

prune334.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

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

sample5.1s

Algorithm

intervals

Results

2.1s	1737×	body	1280	valid
1.2s	1418×	body	640	valid
899.0ms	5000×	body	80	valid
382.0ms	689×	body	320	valid
99.0ms	363×	body	160	valid