Details

sample106.0ms

Algorithm

intervals

Results

46.0ms	57×	body	1280	valid
21.0ms	48×	body	640	valid
16.0ms	155×	body	80	valid
6.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify64.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

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	(/ x (tan B))
4.0ms	(/ 1.0 (sin B))

series393.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
191.0ms	(/ x (tan B))
33.0ms	(/ 1.0 (sin B))

simplify1.7s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	3211
2	739
1	263
0	137

prune486.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma (* (cos B) (/ x (sin B))) (- 1.0) (/ 1.0 (sin B)))
9.0ms	(/ x (sin B))
8.0ms	(/ 1.0 (sin B))
27.0ms	(* (cos B) (/ x (sin B)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(fma (* (cos B) (/ x (sin B))) (- 1.0) (/ 1.0 (sin B)))
70.0ms	(/ x (sin B))
34.0ms	(/ 1.0 (sin B))
96.0ms	(* (cos B) (/ x (sin B)))

simplify1.0s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1642
1	364
0	164

prune644.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
112×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
98×	`add-cube-cbrt`
44×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
19×	`associate-/r*`
16×	`div-exp`
11×	`div-inv`
9×	`associate-/l*`
8×	`cbrt-undiv`
7×	`pow1` `prod-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `cbrt-unprod`
2×	`associate-/r/`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 211

Calls

4 calls:

6.0ms	(/ (sin B) x)
5.0ms	(/ 1.0 (sin B))
37.0ms	(* (cos B) (/ 1 (/ (sin B) x)))
16.0ms	(/ 1 (/ (sin B) x))

series283.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (sin B) x)
37.0ms	(/ 1.0 (sin B))
136.0ms	(* (cos B) (/ 1 (/ (sin B) x)))
60.0ms	(/ 1 (/ (sin B) x))

simplify522.0ms

Counts

223 → 223

Iterations

Iter	Nodes
done	5001
1	773
0	296

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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:

5.0ms	(fma (* (/ (cos B) (sin B)) x) (- 1.0) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
11.0ms	(/ (cos B) (sin B))
24.0ms	(* (/ (cos B) (sin B)) x)

series340.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(fma (* (/ (cos B) (sin B)) x) (- 1.0) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (sin B))
45.0ms	(/ (cos B) (sin B))
81.0ms	(* (/ (cos B) (sin B)) x)

simplify972.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1483
1	370
0	167

prune573.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes218.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.6s	1690×	body	1280	valid
1.2s	4996×	body	80	valid
1.1s	1437×	body	640	valid
817.0ms	710×	body	320	valid
134.0ms	377×	body	160	valid