Details

sample83.0ms

Algorithm

intervals

Results

30.0ms	51×	body	1280	valid
21.0ms	51×	body	640	valid
12.0ms	157×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify55.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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

rewrite66.0ms

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))))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
18.0ms	(* x (/ 1.0 (tan B)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
24.0ms	(/ 1.0 (sin B))
40.0ms	(/ 1.0 (tan B))
119.0ms	(* x (/ 1.0 (tan B)))

simplify1.7s

Counts

147 → 147

Iterations

Useful iterations: done (1.7s)

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

prune398.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite69.0ms

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:

40.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series264.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
19.0ms	(/ 1.0 (sin B))
116.0ms	(/ (* x 1.0) (tan B))

simplify1.4s

Counts

197 → 197

Iterations

Useful iterations: done (1.4s)

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

prune399.0ms

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

rewrite32.0ms

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*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
1×	`pow-prod-down` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

0.0ms	(fma (/ (* x (cos B)) (sin B)) (- 1.0) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
9.0ms	(* x (cos B))
15.0ms	(/ (* x (cos B)) (sin B))

series281.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(fma (/ (* x (cos B)) (sin B)) (- 1.0) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
38.0ms	(* x (cos B))
101.0ms	(/ (* x (cos B)) (sin B))

simplify1.5s

Counts

94 → 94

Iterations

Useful iterations: 3 (589.0ms)

Iter	Nodes	Cost
0	140	902
1	288	876
2	769	770
3	2679	769
done	5001	769

prune254.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

687×	`times-frac`
418×	`add-sqr-sqrt`
410×	`*-un-lft-identity`
401×	`add-cube-cbrt`
338×	`prod-diff`
87×	`div-inv`
32×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`div-exp`
14×	`associate-/r/`
13×	`fma-neg`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
2×	`cbrt-unprod`
1×	`tan-quot` `sub-neg` `flip3--` `pow-flip` `diff-log` `frac-sub` `flip--` `associate-/l/` `inv-pow`

Counts

4 → 486

Calls

4 calls:

62.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
6.0ms	(/ 1.0 (sin B))
9.0ms	(/ (tan B) (* x 1.0))
15.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
25.0ms	(/ 1.0 (sin B))
54.0ms	(/ (tan B) (* x 1.0))
95.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.4s

Counts

498 → 498

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	664	25389
1	1502	19800
2	2865	13907
done	5000	13240

prune518.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes67.0ms

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	10	14
1	11	14
done	11	14

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1726×	body	1280	valid
504.0ms	1395×	body	640	valid
388.0ms	4997×	body	80	valid
170.0ms	715×	body	320	valid
59.0ms	354×	body	160	valid