Details

sample243.0ms

Algorithm

intervals

Results

90.0ms	48×	body	640	valid
57.0ms	53×	body	1280	valid
25.0ms	167×	body	80	valid
11.0ms	24×	body	320	valid
2.0ms	8×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	62
6	62
5	60
4	54
3	43
2	33
1	18
0	10

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
8.0ms	(/ x (tan B))

series379.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
40.0ms	(/ 1.0 (sin B))
161.0ms	(/ x (tan B))

simplify1.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
3	3228
2	740
1	263
0	137

prune465.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-l` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma (* (/ x (sin B)) (cos B)) (- 1.0) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
8.0ms	(/ x (sin B))
21.0ms	(* (/ x (sin B)) (cos B))

series478.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(fma (* (/ x (sin B)) (cos B)) (- 1.0) (/ 1.0 (sin B)))
37.0ms	(/ 1.0 (sin B))
95.0ms	(/ x (sin B))
164.0ms	(* (/ x (sin B)) (cos B))

simplify831.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1419
1	362
0	164

prune615.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
19×	`add-exp-log`
14×	`associate-r`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-l` `div-inv` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `tan-quot` `associate-/r/` `cbrt-unprod`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 112

Calls

4 calls:

0.0ms	(fma (* x (/ 1 (tan B))) (- 1.0) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
17.0ms	(/ 1 (tan B))
32.0ms	(* x (/ 1 (tan B)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(fma (* x (/ 1 (tan B))) (- 1.0) (/ 1.0 (sin B)))
39.0ms	(/ 1.0 (sin B))
37.0ms	(/ 1 (tan B))
177.0ms	(* x (/ 1 (tan B)))

simplify771.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1530
1	394
0	180

prune642.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (/ 1 (sin B)) (cos B))
0.3b	(* x (* (/ 1 (sin B)) (cos B)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
34×	`add-exp-log`
30×	`*-un-lft-identity`
29×	`times-frac` `add-cube-cbrt`
22×	`add-cbrt-cube`
16×	`associate-l`
13×	`prod-exp`
12×	`pow1`
7×	`div-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-r` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 124

Calls

4 calls:

10.0ms	(/ 1 (sin B))
9.0ms	(/ 1.0 (sin B))
32.0ms	(* (/ 1 (sin B)) (cos B))
60.0ms	(* x (* (/ 1 (sin B)) (cos B)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (sin B))
25.0ms	(/ 1.0 (sin B))
46.0ms	(* (/ 1 (sin B)) (cos B))
140.0ms	(* x (* (/ 1 (sin B)) (cos B)))

simplify1.7s

Counts

136 → 136

Iterations

Iter	Nodes
done	5002
2	2384
1	425
0	185

prune761.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.4s	1716×	body	1280	valid
1.3s	4878×	body	80	valid
1.1s	1440×	body	640	valid
528.0ms	709×	body	320	valid
177.0ms	362×	body	160	valid