Details

sample817.0ms

Algorithm

intervals

Results

110.0ms	55×	body	1280	valid
84.0ms	37×	body	640	valid
48.0ms	155×	body	80	valid
19.0ms	19×	body	320	valid
17.0ms	61×	body	80	nan
12.0ms	17×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2024
7	2024
6	1982
5	908
4	393
3	188
2	99
1	47
0	20

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ F (sin B))
6.0b	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
14.1b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite61.0ms

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:

10.0ms	(/ x (tan B))
10.0ms	(/ F (sin B))
29.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
6.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series727.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ x (tan B))
63.0ms	(/ F (sin B))
200.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
312.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	2003
3	2003
2	1641
1	547
0	244

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.5b	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
14.1b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

11.0ms	(/ x (tan B))
18.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
31.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
5.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series768.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ x (tan B))
149.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
210.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
252.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	2000
3	2000
2	1351
1	481
0	220

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.4b	(/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.5b	(/ 1 (/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
14.1b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
36×	`times-frac`
32×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
26×	`div-exp`
20×	`add-cbrt-cube`
15×	`prod-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-l`
6×	`pow-to-exp` `pow1` `pow-exp` `div-inv` `associate-/l*`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 139

Calls

4 calls:

18.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
32.0ms	(/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
17.0ms	(/ 1 (/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series732.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
186.0ms	(/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
132.0ms	(/ 1 (/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
295.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.4s

Counts

151 → 151

Iterations

Iter	Nodes
done	2001
3	2001
2	1817
1	637
0	262

prune2.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.4b	(/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
0.5b	(/ 1 (/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
14.1b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

10.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
8.0ms	(/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
7.0ms	(/ 1 (/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
444.0ms	(/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
321.0ms	(/ 1 (/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
302.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.6s

Counts

169 → 169

Iterations

Iter	Nodes
done	2000
3	2000
2	1912
1	718
0	297

prune3.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.7b

regimes529.0ms

Accuracy

0% (0.6b remaining)

Error of 10.5b against oracle of 9.9b and baseline of 10.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample13.4s

Algorithm

intervals

Results

4.8s	1648×	body	1280	valid
3.3s	1385×	body	640	valid
2.6s	4834×	body	80	valid
1.0s	690×	body	320	valid
890.0ms	1778×	body	80	nan
347.0ms	360×	body	160	valid