Details

sample561.0ms

Algorithm

intervals

Results

142.0ms	55×	body	1280	valid
117.0ms	37×	body	640	valid
67.0ms	155×	body	80	valid
63.0ms	19×	body	320	valid
22.0ms	61×	body	80	nan
16.0ms	17×	body	160	valid

simplify1.7s

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

localize44.0ms

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)

rewrite31.0ms

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	(/ x (tan B))
5.0ms	(/ F (sin B))
15.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
4.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series789.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ x (tan B))
97.0ms	(/ F (sin B))
231.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
294.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.5s

Counts

139 → 139

Iterations

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

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.7b

localize42.0ms

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)

rewrite42.0ms

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:

5.0ms	(/ x (tan B))
14.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
18.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series781.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ x (tan B))
125.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
215.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
299.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.5s

Counts

117 → 117

Iterations

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

prune926.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.7b

localize64.0ms

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)

rewrite46.0ms

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:

9.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
17.0ms	(/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
14.0ms	(/ 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)

series738.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (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))
162.0ms	(/ 1 (/ (sin B) (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
265.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.8s

Counts

151 → 151

Iterations

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

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.7b

localize79.0ms

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)

rewrite44.0ms

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:

22.0ms	(* (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)

series1.1s

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
390.0ms	(/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))))
296.0ms	(/ 1 (/ (sin B) (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F)))))
289.0ms	(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

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.7b

regimes533.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample13.8s

Algorithm

intervals

Results

5.1s	1648×	body	1280	valid
3.2s	4834×	body	80	valid
2.9s	1385×	body	640	valid
1.1s	690×	body	320	valid
776.0ms	1778×	body	80	nan
337.0ms	360×	body	160	valid