Details

sample110.0ms

Algorithm

intervals

Results

42.0ms	60×	body	1280	valid
26.0ms	47×	body	640	valid
15.0ms	138×	body	80	valid
9.0ms	28×	body	320	valid
3.0ms	13×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite95.0ms

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:

32.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
20.0ms	(/ 1.0 (sin B))
11.0ms	(/ 1.0 (tan B))
28.0ms	(* x (/ 1.0 (tan B)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
21.0ms	(/ 1.0 (sin B))
45.0ms	(/ 1.0 (tan B))
128.0ms	(* x (/ 1.0 (tan B)))

simplify2.2s

Counts

147 → 147

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	199	1713
1	446	1635
2	1139	1489
3	3298	1451
done	5000	1440

prune663.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite119.0ms

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:

71.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
10.0ms	(/ 1.0 (sin B))
20.0ms	(/ (* x 1.0) (tan B))

series388.0ms

Counts

3 → 9

Calls

3 calls:

194.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
29.0ms	(/ 1.0 (sin B))
165.0ms	(/ (* x 1.0) (tan B))

simplify2.2s

Counts

197 → 197

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	284	6281
1	640	5115
2	1655	4181
done	5001	3472

prune600.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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

rewrite79.0ms

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:

34.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
20.0ms	(* x (cos B))
6.0ms	(/ 1.0 (sin B))
14.0ms	(/ (* x (cos B)) (sin B))

series398.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
56.0ms	(* x (cos B))
22.0ms	(/ 1.0 (sin B))
149.0ms	(/ (* x (cos B)) (sin B))

simplify4.2s

Counts

127 → 127

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	174	1742
1	393	1688
2	1131	1482
3	4900	1443
done	5000	1443

prune581.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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:

14.0ms	(* x (cos B))
31.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

series181.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(* x (cos B))
115.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

simplify2.9s

Counts

58 → 58

Iterations

Useful iterations: done (2.9s)

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

prune171.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes122.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	1713×	body	1280	valid
1.4s	4910×	body	80	valid
1.3s	1334×	body	640	valid
473.0ms	790×	body	320	valid
123.0ms	383×	body	160	valid