Details

sample549.0ms

Algorithm

intervals

Results

139.0ms	143×	body	80	valid
124.0ms	46×	body	1280	valid
94.0ms	54×	body	640	valid
31.0ms	19×	body	320	valid
18.0ms	48×	body	80	nan
16.0ms	18×	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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ F (sin B))
7.0b	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
17.4b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite33.0ms

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

series691.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ x (tan B))
61.0ms	(/ F (sin B))
219.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
304.0ms	(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

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.5b	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
17.4b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite29.0ms

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:

5.0ms	(/ x (tan B))
9.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
11.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series748.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ x (tan B))
133.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
220.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
269.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.4s

Counts

117 → 117

Iterations

Iter	Nodes
done	2000
3	2000
2	1351
1	481
0	220

prune889.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2))) F) (sin B))
0.7b	(* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))
18.0b	(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
18.0b	(pow (fma x 2 (fma F F 2)) (/ -1/2 2))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
42×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cube-cbrt`
28×	`prod-exp`
26×	`pow-unpow`
24×	`unpow-prod-down`
21×	`times-frac`
15×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
12×	`sqr-pow`
11×	`div-exp`
9×	`unswap-sqr`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `div-inv`
2×	`pow-pow`
1×	`pow2` `clear-num` `frac-2neg` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l`

Counts

4 → 149

Calls

4 calls:

53.0ms	(/ (* (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2))) F) (sin B))
22.0ms	(* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))
3.0ms	(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
3.0ms	(pow (fma x 2 (fma F F 2)) (/ -1/2 2))

series883.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (* (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2))) F) (sin B))
94.0ms	(* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))
306.0ms	(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
279.0ms	(pow (fma x 2 (fma F F 2)) (/ -1/2 2))

simplify1.5s

Counts

161 → 161

Iterations

Iter	Nodes
done	2000
3	2000
2	1759
1	592
0	227

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (pow (fma 2 x (fma F F 2)) -1/2))
0.4b	(/ (sin B) (* F (pow (fma 2 x (fma F F 2)) -1/2)))
0.4b	(/ 1 (/ (sin B) (* F (pow (fma 2 x (fma F F 2)) -1/2))))
17.4b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 139

Calls

4 calls:

9.0ms	(* F (pow (fma 2 x (fma F F 2)) -1/2))
12.0ms	(/ (sin B) (* F (pow (fma 2 x (fma F F 2)) -1/2)))
29.0ms	(/ 1 (/ (sin B) (* F (pow (fma 2 x (fma F F 2)) -1/2))))
5.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series791.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* F (pow (fma 2 x (fma F F 2)) -1/2))
190.0ms	(/ (sin B) (* F (pow (fma 2 x (fma F F 2)) -1/2)))
224.0ms	(/ 1 (/ (sin B) (* F (pow (fma 2 x (fma F F 2)) -1/2))))
250.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify1.7s

Counts

151 → 151

Iterations

Iter	Nodes
done	2003
3	2003
2	1985
1	645
0	266

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

98% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.6b

bsearch859.0ms

Steps

Iters	Range		Point
11	1.2035886760163307e-31	3231.8276777318033	3174.6489492657015
8	-4.3574966463759825e+39	-5.531947254279231e+35	-5.615906575338096e+35

simplify10.0ms

Iterations

Iter	Nodes
done	47
2	47
1	41
0	32

end0.0ms

sample13.3s

Algorithm

intervals

Results

4.7s	1632×	body	1280	valid
3.0s	1351×	body	640	valid
2.5s	4817×	body	80	valid
1.4s	685×	body	320	valid
1.0s	1676×	body	80	nan
346.0ms	377×	body	160	valid