Details

sample165.0ms

Algorithm

intervals

Results

57.0ms	55×	body	1280	valid
54.0ms	53×	body	640	valid
23.0ms	154×	body	80	valid
8.0ms	21×	body	320	valid
3.0ms	10×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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)))

rewrite104.0ms

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:

58.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
10.0ms	(/ 1.0 (sin B))
10.0ms	(/ 1.0 (tan B))
19.0ms	(* x (/ 1.0 (tan B)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
35.0ms	(/ 1.0 (sin B))
63.0ms	(/ 1.0 (tan B))
143.0ms	(* x (/ 1.0 (tan B)))

simplify2.5s

Counts

147 → 147

Iterations

Useful iterations: done (2.5s)

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

prune625.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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))

rewrite91.0ms

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:

49.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
6.0ms	(/ 1.0 (sin B))
15.0ms	(/ (* x 1.0) (tan B))

series420.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
36.0ms	(/ 1.0 (sin B))
184.0ms	(/ (* x 1.0) (tan B))

simplify1.9s

Counts

197 → 197

Iterations

Useful iterations: done (1.9s)

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

prune568.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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)))
9.0ms	(* x (cos B))
6.0ms	(/ 1.0 (sin B))
18.0ms	(/ (* x (cos B)) (sin B))

series339.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(fma (/ (* x (cos B)) (sin B)) (- 1.0) (/ 1.0 (sin B)))
43.0ms	(* x (cos B))
21.0ms	(/ 1.0 (sin B))
134.0ms	(/ (* x (cos B)) (sin B))

simplify2.3s

Counts

94 → 94

Iterations

Useful iterations: 3 (771.0ms)

Iter	Nodes	Cost
0	140	902
1	288	876
2	771	770
3	2679	769
done	5001	769

prune343.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log` `add-cbrt-cube`
13×	`fma-neg` `prod-diff`
9×	`pow1`
6×	`associate-r/` `associate-/r` `associate-/l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `frac-sub` `flip--` `sub-div`

Counts

4 → 123

Calls

4 calls:

44.0ms	(- (/ 1.0 (sin B)) (* x (* 1.0 (/ (cos B) (sin B)))))
11.0ms	(/ 1.0 (sin B))
16.0ms	(/ (cos B) (sin B))
50.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(- (/ 1.0 (sin B)) (* x (* 1.0 (/ (cos B) (sin B)))))
38.0ms	(/ 1.0 (sin B))
22.0ms	(/ (cos B) (sin B))
138.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

simplify1.9s

Counts

135 → 135

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	194	1957
1	442	1881
2	1317	1657
done	5000	1619

prune549.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes117.0ms

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	11	14
done	11	14

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.2s	1706×	body	1280	valid
1.8s	4938×	body	80	valid
1.3s	1451×	body	640	valid
503.0ms	726×	body	320	valid
176.0ms	334×	body	160	valid