Details

sample593.0ms

Algorithm

intervals

Results

188.0ms	65×	body	1280	valid
115.0ms	56×	body	80	nan
70.0ms	34×	body	640	valid
68.0ms	150×	body	80	valid
43.0ms	25×	body	320	valid
6.0ms	7×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
6	1982
5	908
4	393
3	188
2	99
1	47
0	20

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ x (tan B))
5.3b	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
17.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
30×	`times-frac`
22×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
8×	`unpow-prod-down`
7×	`associate-l`
6×	`associate-/r` `prod-exp` `associate-/l` `unswap-sqr`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `pow-exp` `div-inv`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`pow-pow` `tan-quot` `associate-r/` `associate-/r/` `-commutative`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/ F (sin B))
5.0ms	(/ x (tan B))
22.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
7.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series787.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ F (sin B))
185.0ms	(/ x (tan B))
245.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
285.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	2005
2	1645
1	547
0	244

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.5b	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
17.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`times-frac`
16×	`associate-r`
9×	`div-exp`
8×	`associate-l`
7×	`pow1` `unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `tan-quot` `associate-*r/` `associate-/r/` `un-div-inv`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/ x (tan B))
9.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
25.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
4.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series808.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ x (tan B))
147.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
223.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
267.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.0s

Counts

139 → 139

Iterations

Iter	Nodes
done	2008
2	1627
1	605
0	255

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.5b	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
17.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
32×	`prod-exp`
23×	`add-sqr-sqrt` `add-cbrt-cube`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-r`
12×	`times-frac`
10×	`div-exp`
8×	`associate-l` `cbrt-unprod`
7×	`pow1` `unpow-prod-down`
6×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `associate-/l`

Counts

4 → 120

Calls

4 calls:

17.0ms	(/ (* x (cos B)) (sin B))
9.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
27.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series821.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (* x (cos B)) (sin B))
129.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
234.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
321.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify982.0ms

Counts

132 → 132

Iterations

Iter	Nodes
done	2000
2	1856
1	621
0	243

prune989.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.3b	(* x (/ 1 (tan B)))
0.5b	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
17.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
36×	`add-sqr-sqrt`
35×	`prod-exp`
30×	`associate-r`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
20×	`times-frac`
11×	`associate-l`
10×	`div-exp`
9×	`pow1` `cbrt-unprod`
7×	`unpow-prod-down`
6×	`pow-to-exp` `pow-exp` `unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `*-commutative` `sqr-pow`
2×	`pow-prod-down` `associate-*r/` `un-div-inv` `div-inv`
1×	`pow-pow` `tan-quot` `associate-/r/`

Counts

4 → 136

Calls

4 calls:

17.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
28.0ms	(* x (/ 1 (tan B)))
28.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
7.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series840.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
160.0ms	(* x (/ 1 (tan B)))
214.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
338.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.0s

Counts

148 → 148

Iterations

Iter	Nodes
done	2000
2	1944
1	692
0	269

prune832.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 11.1b

regimes583.0ms

Accuracy

0% (0.7b remaining)

Error of 10.9b against oracle of 10.2b and baseline of 10.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample14.6s

Algorithm

intervals

Results

6.0s	1728×	body	1280	valid
2.9s	1338×	body	640	valid
2.7s	4735×	body	80	valid
1.4s	720×	body	320	valid
776.0ms	1709×	body	80	nan
358.0ms	357×	body	160	valid