Details

sample135.0ms

Algorithm

intervals

Results

53.0ms	55×	body	1280	valid
29.0ms	53×	body	640	valid
24.0ms	154×	body	80	valid
9.0ms	21×	body	320	valid
3.0ms	10×	body	160	valid

simplify123.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

30.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
21.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
18.0ms	(* x (/ 1.0 (tan B)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
21.0ms	(/ 1.0 (sin B))
42.0ms	(/ 1.0 (tan B))
184.0ms	(* x (/ 1.0 (tan B)))

simplify2.1s

Counts

113 → 113

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	174	1141
1	383	1074
2	964	996
3	2656	996
done	5000	996

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `div-inv` `difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

41.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
6.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series338.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
21.0ms	(/ 1.0 (sin B))
149.0ms	(/ (* x 1.0) (tan B))

simplify2.3s

Counts

74 → 74

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	143	847
1	316	799
2	870	739
3	3273	739
done	5001	739

prune297.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
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×	`frac-2neg` `associate-*r/` `prod-exp` `clear-num` `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:

26.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
9.0ms	(* x (cos B))
8.0ms	(/ 1.0 (sin B))
17.0ms	(/ (* x (cos B)) (sin B))

series355.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
43.0ms	(* x (cos B))
24.0ms	(/ 1.0 (sin B))
138.0ms	(/ (* x (cos B)) (sin B))

simplify3.1s

Counts

93 → 93

Iterations

Useful iterations: 2 (218.0ms)

Iter	Nodes	Cost
0	149	1006
1	333	964
2	963	863
3	4289	863
done	5000	863

prune344.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

51.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (sin B))
55.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series484.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
27.0ms	(/ 1.0 (sin B))
103.0ms	(/ (* x 1.0) (sin B))
157.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.5s

Counts

101 → 101

Iterations

Useful iterations: 2 (334.0ms)

Iter	Nodes	Cost
0	160	1221
1	390	1156
2	1338	1021
done	5001	1021

prune416.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes76.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14
done	12	14

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.7s	1706×	body	1280	valid
1.9s	1451×	body	640	valid
1.2s	4938×	body	80	valid
365.0ms	726×	body	320	valid
132.0ms	334×	body	160	valid