Details

sample197.0ms

Algorithm

intervals

Results

43.0ms	50×	body	1280	valid
25.0ms	45×	body	640	valid
21.0ms	160×	body	80	valid
6.0ms	18×	body	320	valid
4.0ms	17×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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

rewrite29.0ms

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:

1.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
8.0ms	(/ 1.0 (sin B))
13.0ms	(/ x (tan B))

series390.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
199.0ms	(/ x (tan B))

simplify1.2s

Counts

78 → 78

Iterations

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

prune537.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

0.0ms	(fma (- 1.0) (/ x (/ (sin B) (cos B))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
15.0ms	(/ (sin B) (cos B))
17.0ms	(/ x (/ (sin B) (cos B)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(fma (- 1.0) (/ x (/ (sin B) (cos B))) (/ 1.0 (sin B)))
25.0ms	(/ 1.0 (sin B))
26.0ms	(/ (sin B) (cos B))
123.0ms	(/ x (/ (sin B) (cos B)))

simplify1.3s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
2	2510
1	570
0	242

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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 (- 1.0) (* (/ x (sin B)) (cos B)) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
6.0ms	(/ x (sin B))
15.0ms	(* (/ x (sin B)) (cos B))

series456.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(fma (- 1.0) (* (/ x (sin B)) (cos B)) (/ 1.0 (sin B)))
30.0ms	(/ 1.0 (sin B))
75.0ms	(/ x (sin B))
157.0ms	(* (/ x (sin B)) (cos B))

simplify940.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1419
1	362
0	164

prune759.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

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))
0.2b	(/ 1 (tan B))
0.2b	(* x (/ 1 (tan B)))

rewrite66.0ms

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:

1.0ms	(fma (* x (/ 1 (tan B))) (- 1.0) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
11.0ms	(/ 1 (tan B))
40.0ms	(* x (/ 1 (tan B)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(fma (* x (/ 1 (tan B))) (- 1.0) (/ 1.0 (sin B)))
42.0ms	(/ 1.0 (sin B))
58.0ms	(/ 1 (tan B))
158.0ms	(* x (/ 1 (tan B)))

simplify804.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1530
1	394
0	180

prune631.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes177.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.6s	1686×	body	1280	valid
1.4s	4889×	body	80	valid
1.3s	1451×	body	640	valid
418.0ms	675×	body	320	valid
118.0ms	358×	body	160	valid