Details

sample540.0ms

Algorithm

intervals

Results

175.0ms	57×	body	1280	valid
84.0ms	29×	body	320	valid
81.0ms	44×	body	640	valid
54.0ms	145×	body	80	valid
20.0ms	60×	body	80	nan
6.0ms	8×	body	160	valid

simplify3.4s

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: 8.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ x (tan B))
3.6b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
15.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite52.0ms

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	(/ F (sin B))
5.0ms	(/ x (tan B))
33.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
6.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series772.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ F (sin B))
144.0ms	(/ x (tan B))
242.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
297.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify1.9s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	1640
1	547
0	244

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 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)
15.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite49.0ms

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))
26.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
9.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series845.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ x (tan B))
214.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
158.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
331.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify3.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4779
2	1354
1	481
0	220

prune887.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
0.2b	(/ (log1p (expm1 (* (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)
15.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite19.0ms

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×	`pow1` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `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` `expm1-log1p` `clear-num` `pow-pow` `frac-2neg` `div-exp` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef`

Counts

4 → 90

Calls

4 calls:

0.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
5.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
9.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

201.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
567.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
140.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
256.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5019
3	2971
2	1005
1	406
0	190

prune859.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (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)
15.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`add-exp-log`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt`
17×	`associate-r`
16×	`add-cbrt-cube`
14×	`times-frac`
10×	`associate-l` `prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`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×	`rec-exp` `clear-num` `pow-pow` `frac-2neg` `1-exp` `pow-prod-down` `tan-quot` `associate-r/` `associate-/r/` `un-div-inv` `associate-/l`

Counts

4 → 114

Calls

4 calls:

18.0ms	(* x (/ 1 (tan B)))
15.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
12.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series814.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* x (/ 1 (tan B)))
223.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
136.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
296.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify1.7s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1643
1	576
0	242

prune883.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.8b

regimes501.0ms

Accuracy

0% (0.7b remaining)

Error of 10.5b against oracle of 9.8b and baseline of 10.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample13.5s

Algorithm

intervals

Results

5.4s	1633×	body	1280	valid
3.0s	1364×	body	640	valid
2.8s	4807×	body	80	valid
890.0ms	686×	body	320	valid
790.0ms	1747×	body	80	nan
299.0ms	349×	body	160	valid