Details

sample143.0ms

Algorithm

intervals

Results

44.0ms	86×	body	1280	valid
31.0ms	264×	body	80	valid
29.0ms	78×	body	640	valid
10.0ms	36×	body	320	valid
4.0ms	23×	body	160	valid

simplify135.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
0.4b	(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
92×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/`

Counts

2 → 149

Calls

2 calls:

13.0ms	(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
8.0ms	(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

series420.0ms

Counts

2 → 6

Calls

2 calls:

305.0ms	(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
116.0ms	(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

simplify1.6s

Counts

155 → 155

Iterations

Iter	Nodes
done	5001
2	1436
1	547
0	225

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-r` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

2 → 85

Calls

2 calls:

34.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
10.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series480.0ms

Counts

2 → 6

Calls

2 calls:

307.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
172.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify2.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	5005
3	2715
2	799
1	272
0	126

prune574.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ a1 (sqrt 2.0)) a1 (/ (* a2 a2) (sqrt 2.0)))
0.2b	(* (cos th) (fma (/ a1 (sqrt 2.0)) a1 (/ (* a2 a2) (sqrt 2.0))))
0.3b	(/ (* a2 a2) (sqrt 2.0))
0.4b	(/ a1 (sqrt 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`times-frac`
18×	`sqrt-prod`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `fma-udef`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma (/ a1 (sqrt 2.0)) a1 (/ (* a2 a2) (sqrt 2.0)))
13.0ms	(* (cos th) (fma (/ a1 (sqrt 2.0)) a1 (/ (* a2 a2) (sqrt 2.0))))
14.0ms	(/ (* a2 a2) (sqrt 2.0))
10.0ms	(/ a1 (sqrt 2.0))

series762.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(fma (/ a1 (sqrt 2.0)) a1 (/ (* a2 a2) (sqrt 2.0)))
398.0ms	(* (cos th) (fma (/ a1 (sqrt 2.0)) a1 (/ (* a2 a2) (sqrt 2.0))))
75.0ms	(/ (* a2 a2) (sqrt 2.0))
71.0ms	(/ a1 (sqrt 2.0))

simplify2.9s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
3	4251
2	1001
1	342
0	158

prune685.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
624×	`add-sqr-sqrt`
577×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-r`
34×	`associate-/l*`
22×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

3 → 706

Calls

3 calls:

168.0ms	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
12.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
35.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series1.0s

Counts

3 → 9

Calls

3 calls:

318.0ms	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
559.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
153.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify3.3s

Counts

715 → 715

Iterations

Iter	Nodes
done	5070
2	3976
1	1623
0	600

prune3.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes456.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	2543×	body	1280	valid
1.5s	2145×	body	640	valid
1.3s	8005×	body	80	valid
342.0ms	1061×	body	320	valid
201.0ms	522×	body	160	valid