Details

sample168.0ms

Algorithm

intervals

Results

52.0ms	294×	body	80	valid
44.0ms	74×	body	1280	valid
27.0ms	61×	body	640	valid
8.0ms	28×	body	320	valid
3.0ms	13×	body	160	valid

simplify273.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	175
8	175
7	173
6	151
5	132
4	114
3	87
2	57
1	26
0	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.3b	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.3b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
33.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
6.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series544.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(fma a1 a1 (* a2 a2))
339.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
142.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	2126
1	276
0	131

prune535.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0)))
0.3b	(/ (cos th) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))
0.3b	(* (/ (cos th) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))))
5.5b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac`
188×	`add-sqr-sqrt`
114×	`sqrt-prod`
113×	`*-un-lft-identity` `add-cube-cbrt`
90×	`cbrt-prod`
58×	`associate-r`
47×	`add-exp-log`
36×	`add-cbrt-cube`
26×	`associate-l`
21×	`unswap-sqr`
20×	`cbrt-undiv` `div-exp`
16×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod` `div-inv`
9×	`associate-/l*`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `hypot-def`

Counts

4 → 284

Calls

4 calls:

18.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0)))
26.0ms	(/ (cos th) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))
119.0ms	(* (/ (cos th) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))))
3.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

377.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0)))
803.0ms	(/ (cos th) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))
443.0ms	(* (/ (cos th) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))))
60.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify581.0ms

Counts

296 → 296

Iterations

Iter	Nodes
done	5000
1	1056
0	356

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (hypot a1 a2))
0.2b	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
0.2b	(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(* (/ (hypot a1 a2) (cbrt (sqrt 2.0))) (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `add-exp-log`
59×	`times-frac`
48×	`*-un-lft-identity` `add-cube-cbrt`
44×	`cbrt-prod`
43×	`add-cbrt-cube`
34×	`associate-l`
23×	`prod-exp` `cbrt-unprod`
22×	`sqrt-prod`
18×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
8×	`pow1` `associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`frac-times` `associate-l/` `associate-r/`

Counts

4 → 170

Calls

4 calls:

13.0ms	(* (cos th) (hypot a1 a2))
11.0ms	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
27.0ms	(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
97.0ms	(* (/ (hypot a1 a2) (cbrt (sqrt 2.0))) (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (cos th) (hypot a1 a2))
482.0ms	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
919.0ms	(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
321.0ms	(* (/ (hypot a1 a2) (cbrt (sqrt 2.0))) (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))))

simplify1.9s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
2	4130
1	626
0	229

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite285.0ms

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:

30.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))
143.0ms	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

series709.0ms

Counts

3 → 9

Calls

3 calls:

162.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
183.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))
364.0ms	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

simplify1.1s

Counts

715 → 715

Iterations

Iter	Nodes
done	5000
1	1689
0	600

prune2.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes490.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	23
2	23
1	21
0	16

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.0s	8054×	body	80	valid
1.8s	2437×	body	1280	valid
1.1s	2105×	body	640	valid
481.0ms	1058×	body	320	valid
111.0ms	550×	body	160	valid