Details

sample158.0ms

Algorithm

intervals

Results

76.0ms	59×	body	1280	valid
27.0ms	43×	body	640	valid
21.0ms	146×	body	80	valid
13.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

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:

44.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
12.0ms	(/ 1.0 (tan B))
12.0ms	(/ 1.0 (sin B))
49.0ms	(* x (/ 1.0 (tan B)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
57.0ms	(/ 1.0 (tan B))
24.0ms	(/ 1.0 (sin B))
164.0ms	(* x (/ 1.0 (tan B)))

simplify1.1s

Counts

113 → 113

Iterations

Useful iterations: 2 (339.0ms)

Iter	Nodes	Cost
0	174	1141
1	409	1078
2	1459	996
done	5001	996

prune506.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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))
0.1b	(/ (* x 1.0) (tan B))

rewrite66.0ms

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:

47.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
6.0ms	(/ 1.0 (sin B))
12.0ms	(/ (* x 1.0) (tan B))

series420.0ms

Counts

3 → 9

Calls

3 calls:

213.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
27.0ms	(/ 1.0 (sin B))
180.0ms	(/ (* x 1.0) (tan B))

simplify982.0ms

Counts

74 → 74

Iterations

Useful iterations: 2 (205.0ms)

Iter	Nodes	Cost
0	143	847
1	337	799
2	1401	739
done	5000	739

prune334.0ms

Pruning

9 alts after pruning (9 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 (/ (* x (cos B)) (sin B))))
0.1b	(/ 1.0 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite65.0ms

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:

32.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
6.0ms	(/ 1.0 (sin B))
10.0ms	(* x (cos B))
13.0ms	(/ (* x (cos B)) (sin B))

series405.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
41.0ms	(/ 1.0 (sin B))
64.0ms	(* x (cos B))
137.0ms	(/ (* x (cos B)) (sin B))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	149	1006
1	354	964
2	1465	869
done	5001	863

prune359.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

10.0ms	(* x (cos B))
16.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

series183.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(* x (cos B))
112.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

simplify655.0ms

Counts

54 → 54

Iterations

Useful iterations: done (653.0ms)

Iter	Nodes	Cost
0	103	734
1	238	711
2	921	645
done	5000	641

prune132.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	11	11
done	11	11

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.3s	1742×	body	1280	valid
1.8s	1462×	body	640	valid
1.0s	647×	body	320	valid
889.0ms	4957×	body	80	valid
127.0ms	365×	body	160	valid