Details

sample397.0ms

Algorithm

intervals

Results

110.0ms	50×	body	1280	valid
102.0ms	54×	body	640	valid
41.0ms	147×	body	80	valid
18.0ms	74×	body	80	nan
15.0ms	17×	body	320	valid
9.0ms	14×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ F (sin B))
7.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
19.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite34.0ms

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))
18.0ms	(* (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)

series752.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ x (tan B))
70.0ms	(/ F (sin B))
239.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
323.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.4s

Counts

139 → 139

Iterations

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

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
19.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

9.0ms	(/ 1 (sin B))
27.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
14.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
4.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series647.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ 1 (sin B))
210.0ms	(* (* (pow (fma x 2 (fma F F 2)) -1/2) F) (/ 1 (sin B)))
130.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
284.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	2002
3	2002
2	1502
1	548
0	221

prune2.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.7b

localize76.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
7.2b	(* (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)) (/ F (sin B)))
19.0b	(sqrt (fma x 2 (fma F F 2)))
19.0b	(sqrt (fma x 2 (fma F F 2)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
58×	`add-sqr-sqrt`
47×	`prod-exp`
44×	`unpow-prod-down`
28×	`sqrt-prod`
25×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
18×	`pow-to-exp` `add-cbrt-cube` `pow-exp` `unswap-sqr`
12×	`swap-sqr` `sqr-pow`
11×	`associate-l`
10×	`times-frac` `div-exp`
8×	`pow1`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative`
1×	`pow2` `associate-*r/` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 158

Calls

4 calls:

15.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
55.0ms	(* (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)) (/ F (sin B)))
2.0ms	(sqrt (fma x 2 (fma F F 2)))
2.0ms	(sqrt (fma x 2 (fma F F 2)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
201.0ms	(* (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)) (/ F (sin B)))
166.0ms	(sqrt (fma x 2 (fma F F 2)))
154.0ms	(sqrt (fma x 2 (fma F F 2)))

simplify1.4s

Counts

170 → 170

Iterations

Iter	Nodes
done	2002
3	2002
2	1551
1	527
0	204

prune2.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 10.7b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* (/ x (sin B)) (cos B))
7.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
19.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

5.0ms	(/ F (sin B))
14.0ms	(* (/ x (sin B)) (cos B))
27.0ms	(* (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)

series794.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ F (sin B))
182.0ms	(* (/ x (sin B)) (cos B))
263.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
261.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.6s

Counts

143 → 143

Iterations

Iter	Nodes
done	2001
3	2001
2	1932
1	603
0	252

prune2.3s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 10.7b

regimes498.0ms

Accuracy

76.8% (0.7b remaining)

Error of 10.8b against oracle of 10.1b and baseline of 13.2b

bsearch296.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.006279617967676429
5	-2544079.157399237	-994084.4405169716	-1004873.6803424847

simplify9.0ms

Iterations

Iter	Nodes
done	45
1	45
0	38

end0.0ms

sample13.4s

Algorithm

intervals

Results

5.1s	1636×	body	1280	valid
3.2s	4772×	body	80	valid
2.7s	1395×	body	640	valid
978.0ms	695×	body	320	valid
725.0ms	1707×	body	80	nan
315.0ms	367×	body	160	valid