Details

sample133.0ms

Algorithm

intervals

Results

68.0ms	50×	body	1280	valid
19.0ms	39×	body	640	valid
19.0ms	173×	body	80	valid
9.0ms	26×	body	320	valid
2.0ms	10×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`times-frac` `add-cube-cbrt`
14×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`clear-num` `sum-log` `frac-2neg` `prod-exp` `tan-quot` `associate-*r/` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `+-commutative` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `associate-+l-` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

20.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
7.0ms	(/ 1.0 (sin B))
7.0ms	(/ 1.0 (tan B))
32.0ms	(* x (/ 1.0 (tan B)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
48.0ms	(/ 1.0 (tan B))
168.0ms	(* x (/ 1.0 (tan B)))

simplify786.0ms

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1638
1	444
0	181

prune736.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

55.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
7.0ms	(/ 1.0 (sin B))
9.0ms	(/ (* x 1.0) (tan B))

series300.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
29.0ms	(/ 1.0 (sin B))
137.0ms	(/ (* x 1.0) (tan B))

simplify677.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1506
1	358
0	145

prune466.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `sum-log` `frac-2neg` `associate-*l/`
1×	`neg-sub0` `+-commutative` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `associate-+l-` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

15.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
10.0ms	(/ (* x 1.0) (sin B))
14.0ms	(/ 1.0 (sin B))
24.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series370.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
63.0ms	(/ (* x 1.0) (sin B))
28.0ms	(/ 1.0 (sin B))
167.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify884.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	2328
1	448
0	166

prune614.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

20.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* (cos B) x) (sin B))))
5.0ms	(/ 1.0 (sin B))
10.0ms	(/ (* (cos B) x) (sin B))
11.0ms	(* (cos B) x)

series286.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* (cos B) x) (sin B))))
31.0ms	(/ 1.0 (sin B))
88.0ms	(/ (* (cos B) x) (sin B))
41.0ms	(* (cos B) x)

simplify1.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1805
1	380
0	159

prune446.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.0s	1734×	body	1280	valid
1.2s	1499×	body	640	valid
1.1s	4856×	body	80	valid
367.0ms	681×	body	320	valid
139.0ms	379×	body	160	valid