Details

sample562.0ms

Algorithm

intervals

Results

189.0ms	57×	body	1280	valid
102.0ms	155×	body	80	valid
74.0ms	39×	body	640	valid
30.0ms	22×	body	320	valid
27.0ms	55×	body	80	nan
6.0ms	6×	body	160	valid

simplify7.8s

Counts

1 → 1

Iterations

Iter	Nodes
7	7678
6	1967
5	632
4	261
3	141
2	88
1	47
0	20

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
0.4b	(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
17.0b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

5.0ms	(/ x (tan B))
24.0ms	(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
12.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
6.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series823.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ x (tan B))
226.0ms	(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
170.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
274.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.2s

Counts

162 → 162

Iterations

Iter	Nodes
3	4568
2	1466
1	577
0	271

prune2.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
17.0b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite55.0ms

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:

10.0ms	(/ x (tan B))
21.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
17.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series884.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ x (tan B))
248.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
146.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
331.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.0s

Counts

117 → 117

Iterations

Iter	Nodes
3	5058
2	1247
1	457
0	220

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x (cos B)) (sin B))
0.2b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
17.0b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

16.0ms	(/ (* x (cos B)) (sin B))
11.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
8.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series860.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (* x (cos B)) (sin B))
271.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
129.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
312.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.6s

Counts

110 → 110

Iterations

Iter	Nodes
3	6477
2	1424
1	470
0	206

prune1.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x (cos B)) (sin B))
0.2b	(/ 1 (/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F)))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
17.0b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
36×	`times-frac`
32×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
24×	`div-exp`
20×	`add-cbrt-cube`
13×	`prod-exp`
10×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-l`
6×	`pow1` `div-inv`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `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 → 137

Calls

4 calls:

16.0ms	(/ (* x (cos B)) (sin B))
15.0ms	(/ 1 (/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F)))
19.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
5.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series729.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (* x (cos B)) (sin B))
145.0ms	(/ 1 (/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F)))
138.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
307.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify5.5s

Counts

149 → 149

Iterations

Iter	Nodes
3	9302
2	1817
1	635
0	274

prune2.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.3b

regimes482.0ms

Accuracy

0% (0.7b remaining)

Error of 10.8b against oracle of 10.2b and baseline of 10.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample12.4s

Algorithm

intervals

Results

4.4s	1631×	body	1280	valid
2.8s	1441×	body	640	valid
2.5s	4780×	body	80	valid
1.1s	1673×	body	80	nan
969.0ms	692×	body	320	valid
285.0ms	327×	body	160	valid