Details

sample569.0ms

Algorithm

intervals

Results

149.0ms	53×	body	1280	valid
108.0ms	161×	body	80	valid
104.0ms	31×	body	640	valid
41.0ms	28×	body	320	valid
26.0ms	60×	body	80	nan
12.0ms	13×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ F (sin B))
9.0b	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
19.4b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite56.0ms

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:

7.0ms	(/ x (tan B))
10.0ms	(/ F (sin B))
30.0ms	(* (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)

series770.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ x (tan B))
93.0ms	(/ F (sin B))
230.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
315.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.6s

Counts

139 → 139

Iterations

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

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.7b	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
19.4b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite57.0ms

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))
19.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
22.0ms	(/ (* (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)

series930.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ x (tan B))
149.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
255.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
328.0ms	(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

prune949.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.7b	(/ (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))) (sin B))
4.0b	(log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))
19.4b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
5.0ms	(/ (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))) (sin B))
0.0ms	(log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series1.4s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
665.0ms	(/ (expm1 (log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))) (sin B))
243.0ms	(log1p (* (pow (fma x 2 (fma F F 2)) -1/2) F))
326.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	2002
3	2002
2	1011
1	412
0	192

prune948.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.7b	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
19.4b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

30.0ms	(* (/ x (sin B)) (cos B))
16.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
20.0ms	(/ (* (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)

series911.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (/ x (sin B)) (cos B))
149.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
252.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
333.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify2.1s

Counts

121 → 121

Iterations

Iter	Nodes
done	2011
3	2011
2	1597
1	533
0	227

prune975.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

regimes491.0ms

Accuracy

59.4% (2.3b remaining)

Error of 7.6b against oracle of 5.2b and baseline of 11.0b

bsearch229.0ms

Steps

Iters	Range		Point
7	-2.3185489169271762e+172	-7.620507432988769e+170	-7.71339148553278e+170

simplify29.0ms

Iterations

Iter	Nodes
done	38
1	38
0	33

end0.0ms

sample14.5s

Algorithm

intervals

Results

5.7s	1681×	body	1280	valid
3.5s	1442×	body	640	valid
2.8s	4781×	body	80	valid
1.0s	700×	body	320	valid
713.0ms	1697×	body	80	nan
360.0ms	304×	body	160	valid