Details

sample444.0ms

Algorithm

intervals

Results

138.0ms	46×	body	1280	valid
68.0ms	43×	body	640	valid
50.0ms	166×	body	80	valid
18.0ms	72×	body	80	nan
15.0ms	18×	body	320	valid
9.0ms	14×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
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: 16.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ F (sin B))
7.8b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
19.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite39.0ms

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))
23.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series715.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ x (tan B))
75.0ms	(/ F (sin B))
219.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
268.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	1636
1	547
0	244

prune903.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.4b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
19.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite64.0ms

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))
18.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
30.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series830.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ x (tan B))
122.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
218.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
323.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.9s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
3	4694
2	1353
1	481
0	220

prune943.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.4b	(/ (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
2.9b	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
19.4b	(pow (fma 2 x (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:

14.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
5.0ms	(/ (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
0.0ms	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.3s

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
651.0ms	(/ (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
216.0ms	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
294.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5029
3	3084
2	1011
1	412
0	192

prune808.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.4b	(* (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (/ 1 (sin B)))
2.9b	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
19.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
19×	`add-exp-log`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`associate-r`
11×	`times-frac` `add-cbrt-cube`
10×	`associate-l`
7×	`pow1` `unpow-prod-down` `prod-exp`
6×	`unswap-sqr`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `cbrt-unprod` `sqr-pow`
2×	`pow-to-exp` `div-exp` `pow-exp` `*-commutative`
1×	`cbrt-undiv` `rec-exp` `log1p-udef` `pow-pow` `1-exp` `pow-prod-down` `log1p-expm1` `associate-*r/` `un-div-inv` `div-inv`

Counts

4 → 99

Calls

4 calls:

9.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
12.0ms	(* (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (/ 1 (sin B)))
0.0ms	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
576.0ms	(* (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (/ 1 (sin B)))
198.0ms	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
272.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify3.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	5026
3	4059
2	1277
1	502
0	213

prune714.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.3b

regimes414.0ms

Accuracy

66.8% (2.0b remaining)

Error of 7.2b against oracle of 5.2b and baseline of 11.3b

bsearch148.0ms

Steps

Iters	Range		Point
6	-4.775759295698364e+129	-6.044974621018595e+128	-4.7112453216261304e+129

simplify18.0ms

Iterations

Iter	Nodes
done	42
1	42
0	35

end0.0ms

sample9.7s

Algorithm

intervals

Results

3.3s	1676×	body	1280	valid
2.4s	4801×	body	80	valid
2.0s	1391×	body	640	valid
868.0ms	1595×	body	80	nan
553.0ms	670×	body	320	valid
212.0ms	392×	body	160	valid