Details

sample78.0ms

Algorithm

intervals

Results

32.0ms	56×	body	1280	valid
14.0ms	180×	body	80	valid
13.0ms	37×	body	640	valid
6.0ms	24×	body	320	valid
1.0ms	7×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	59	11
6	61	11
done	61	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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))
0.2b	(/ 1.0 (sin B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-r`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
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 → 135

Calls

4 calls:

31.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
5.0ms	(/ 1.0 (tan B))
5.0ms	(/ 1.0 (sin B))
17.0ms	(* x (/ 1.0 (tan B)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
39.0ms	(/ 1.0 (tan B))
19.0ms	(/ 1.0 (sin B))
111.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	199	1713
1	446	1635
2	1138	1489
3	3282	1451
done	5000	1440

prune379.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 188

Calls

3 calls:

38.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
12.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ 1.0 (sin B))

series269.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
118.0ms	(/ (* x 1.0) (tan B))
26.0ms	(/ 1.0 (sin B))

simplify1.4s

Counts

197 → 197

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	284	6281
1	640	5115
2	1652	4181
done	5000	3472

prune407.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
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 → 115

Calls

4 calls:

29.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
11.0ms	(* x (cos B))
12.0ms	(/ (* x (cos B)) (sin B))
6.0ms	(/ 1.0 (sin B))

series280.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
42.0ms	(* x (cos B))
99.0ms	(/ (* x (cos B)) (sin B))
20.0ms	(/ 1.0 (sin B))

simplify2.4s

Counts

127 → 127

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	174	1742
1	393	1688
2	1128	1482
3	4881	1443
done	5000	1443

prune332.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 52

Calls

2 calls:

9.0ms	(* x (cos B))
16.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

series121.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(* x (cos B))
84.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

simplify1.8s

Counts

58 → 58

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	107	768
1	236	743
2	644	673
3	2136	672
done	5001	670

prune138.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes54.0ms

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

sample2.6s

Algorithm

intervals

Results

1.2s	1742×	body	1280	valid
509.0ms	1409×	body	640	valid
396.0ms	4896×	body	80	valid
189.0ms	744×	body	320	valid
58.0ms	340×	body	160	valid