Details

sample514.0ms

Algorithm

intervals

Results

148.0ms	47×	body	1280	valid
82.0ms	45×	body	640	valid
63.0ms	155×	body	80	valid
63.0ms	57×	body	80	nan
26.0ms	20×	body	320	valid
9.0ms	11×	body	160	valid

simplify978.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ F (sin B))
9.8b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
18.7b	(pow (fma 2 x (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` `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 → 123

Calls

4 calls:

4.0ms	(/ x (tan B))
4.0ms	(/ F (sin B))
15.0ms	(* (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)

series784.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ x (tan B))
71.0ms	(/ F (sin B))
230.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
310.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.8s

Counts

135 → 135

Iterations

Iter	Nodes
3	4443
2	1373
1	512
0	240

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.5b

localize33.0ms

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)
0.7b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
18.7b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite50.0ms

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` `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 → 101

Calls

4 calls:

10.0ms	(/ x (tan B))
23.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
14.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series836.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ x (tan B))
159.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
228.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
283.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.8s

Counts

113 → 113

Iterations

Iter	Nodes
3	4667
2	1227
1	451
0	216

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.5b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.7b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
18.7b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite66.0ms

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` `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 → 94

Calls

4 calls:

21.0ms	(/ (* x (cos B)) (sin B))
15.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
19.0ms	(/ (* (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)

series796.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (* x (cos B)) (sin B))
145.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
219.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
257.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify3.2s

Counts

106 → 106

Iterations

Iter	Nodes
3	6344
2	1412
1	464
0	202

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
0.7b	(/ (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F) (sin B))
18.7b	(sqrt (fma 2 x (fma F F 2)))
18.7b	(sqrt (fma 2 x (fma F F 2)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
50×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`prod-exp` `sqrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
16×	`unswap-sqr`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `swap-sqr` `pow-exp` `sqr-pow`
11×	`div-exp`
10×	`associate-r` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `times-frac`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `clear-num` `frac-2neg` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `associate-/l`

Counts

4 → 135

Calls

4 calls:

14.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
49.0ms	(/ (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F) (sin B))
2.0ms	(sqrt (fma 2 x (fma F F 2)))
2.0ms	(sqrt (fma 2 x (fma F F 2)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
205.0ms	(/ (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F) (sin B))
137.0ms	(sqrt (fma 2 x (fma F F 2)))
116.0ms	(sqrt (fma 2 x (fma F F 2)))

simplify4.2s

Counts

147 → 147

Iterations

Iter	Nodes
3	7550
2	1415
1	442
0	184

prune2.1s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 11.5b

regimes439.0ms

Accuracy

0% (0.5b remaining)

Error of 10.4b against oracle of 9.9b and baseline of 10.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	17
1	17
0	15

end0.0ms

sample14.3s

Algorithm

intervals

Results

5.4s	1695×	body	1280	valid
3.6s	1357×	body	640	valid
2.5s	4754×	body	80	valid
1.2s	707×	body	320	valid
768.0ms	1757×	body	80	nan
482.0ms	365×	body	160	valid