Details

sample426.0ms

Algorithm

intervals

Results

154.0ms	53×	body	1280	valid
93.0ms	44×	body	640	valid
50.0ms	152×	body	80	valid
23.0ms	19×	body	320	valid
17.0ms	60×	body	80	nan
9.0ms	13×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2046
5	644
4	269
3	138
2	87
1	45
0	20

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ F (sin B))
4.8b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
16.4b	(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))
15.0ms	(* (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)

series680.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ x (tan B))
55.0ms	(/ F (sin B))
240.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
267.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.4s

Counts

139 → 139

Iterations

Iter	Nodes
3	4249
2	1379
1	517
0	244

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.9b

localize65.0ms

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)
0.5b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
16.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite66.0ms

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))
26.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
23.0ms	(/ (* (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)

series795.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ x (tan B))
157.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
221.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
279.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.8s

Counts

117 → 117

Iterations

Iter	Nodes
3	4742
2	1239
1	456
0	220

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.9b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.5b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
16.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite69.0ms

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:

23.0ms	(/ (* x (cos B)) (sin B))
17.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
23.0ms	(/ (* (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)

series813.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (* x (cos B)) (sin B))
130.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
266.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
287.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify3.2s

Counts

110 → 110

Iterations

Iter	Nodes
3	6287
2	1422
1	469
0	206

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.9b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.3b	(* x (/ (cos B) (sin B)))
0.5b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
16.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `associate-r`
13×	`times-frac`
10×	`associate-l`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
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-r/` `associate-/l`

Counts

4 → 109

Calls

4 calls:

13.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
24.0ms	(* x (/ (cos B) (sin B)))
22.0ms	(/ (* (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)

series844.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
160.0ms	(* x (/ (cos B) (sin B)))
234.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
344.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify4.3s

Counts

121 → 121

Iterations

Iter	Nodes
3	5842
2	1534
1	528
0	229

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.9b

regimes392.0ms

Accuracy

0% (1.2b remaining)

Error of 11.7b against oracle of 10.5b and baseline of 11.7b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	20
1	20
0	18

end0.0ms

sample14.2s

Algorithm

intervals

Results

5.3s	1641×	body	1280	valid
3.0s	4812×	body	80	valid
3.0s	1416×	body	640	valid
1.1s	702×	body	320	valid
750.0ms	1656×	body	80	nan
685.0ms	341×	body	160	valid