Details

sample327.0ms

Algorithm

intervals

Results

36.0ms	60×	body	1280	valid
14.0ms	41×	body	640	valid
13.0ms	169×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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

rewrite32.0ms

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))
12.0ms	(* x (/ 1.0 (tan B)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
40.0ms	(/ 1.0 (tan B))
125.0ms	(* x (/ 1.0 (tan B)))

simplify622.0ms

Counts

115 → 115

Iterations

Useful iterations: 2 (138.0ms)

Iter	Nodes	Cost
0	180	1184
1	427	1125
2	1554	1022
done	5000	1022

prune316.0ms

Pruning

7 alts after pruning (7 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))
0.1b	(/ (* x 1.0) (tan B))

rewrite39.0ms

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:

32.0ms	(+ (- (/ (* 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:

113.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
109.0ms	(/ (* x 1.0) (tan B))

simplify489.0ms

Counts

74 → 74

Iterations

Useful iterations: done (486.0ms)

Iter	Nodes	Cost
0	144	837
1	347	797
2	1259	711
done	5000	706

prune195.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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))

rewrite21.0ms

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))

series252.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
35.0ms	(* x (cos B))
95.0ms	(/ (* x (cos B)) (sin B))

simplify531.0ms

Counts

94 → 94

Iterations

Useful iterations: done (529.0ms)

Iter	Nodes	Cost
0	154	1045
1	370	1002
2	1371	886
done	5000	885

prune244.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
20.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series574.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (/ 1.0 (sin B)))
130.0ms	(cbrt (/ 1.0 (sin B)))
133.0ms	(cbrt (/ 1.0 (sin B)))
177.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify529.0ms

Counts

156 → 156

Iterations

Useful iterations: done (522.0ms)

Iter	Nodes	Cost
0	170	2245
1	306	2086
2	1160	1991
done	5001	1975

prune518.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

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

1.0s	1689×	body	1280	valid
529.0ms	1426×	body	640	valid
391.0ms	4929×	body	80	valid
192.0ms	743×	body	320	valid
69.0ms	352×	body	160	valid