Details

sample140.0ms

Algorithm

intervals

Results

41.0ms	79×	body	640	valid
36.0ms	64×	body	1280	valid
21.0ms	245×	body	80	valid
8.0ms	27×	body	320	valid
4.0ms	21×	body	160	valid

simplify292.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	57	12
3	87	12
4	114	12
5	132	12
6	150	12
7	170	12
8	172	12
done	172	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

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

series492.0ms

Counts

2 → 6

Calls

2 calls:

151.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
341.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.2s

Counts

57 → 57

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	100	839
1	198	806
2	744	692
3	3458	674
done	5000	673

prune224.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 85

Calls

2 calls:

22.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
7.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series442.0ms

Counts

2 → 6

Calls

2 calls:

319.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
123.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify2.5s

Counts

91 → 91

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	126	1508
1	249	1426
2	837	1240
3	2866	1232
done	5000	1228

prune410.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (hypot a1 a2))
0.3b	(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
0.4b	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
5.9b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

81×	`sqrt-prod`
72×	`times-frac`
63×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
43×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`*-commutative` `div-inv`
1×	`rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num` `fma-udef` `hypot-def` `unswap-sqr`

Counts

4 → 161

Calls

4 calls:

19.0ms	(* (cos th) (hypot a1 a2))
63.0ms	(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
15.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series855.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (cos th) (hypot a1 a2))
441.0ms	(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
169.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
88.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify2.5s

Counts

173 → 173

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	194	3009
1	434	2697
2	1513	1918
done	5000	1912

prune729.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma a1 a1 (* a2 a2)) 2.0)
0.1b	(* (cos th) (hypot a1 a2))
0.3b	(* (* (cos th) (hypot a1 a2)) (sqrt (/ (fma a1 a1 (* a2 a2)) 2.0)))
6.0b	(sqrt (/ (fma a1 a1 (* a2 a2)) 2.0))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
26×	`sqrt-prod`
19×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
12×	`pow1`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`rem-sqrt-square` `sqrt-div` `*-commutative`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `div-exp` `clear-num` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

11.0ms	(/ (fma a1 a1 (* a2 a2)) 2.0)
19.0ms	(* (cos th) (hypot a1 a2))
68.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (/ (fma a1 a1 (* a2 a2)) 2.0)))
4.0ms	(sqrt (/ (fma a1 a1 (* a2 a2)) 2.0))

series704.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (fma a1 a1 (* a2 a2)) 2.0)
154.0ms	(* (cos th) (hypot a1 a2))
355.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (/ (fma a1 a1 (* a2 a2)) 2.0)))
124.0ms	(sqrt (/ (fma a1 a1 (* a2 a2)) 2.0))

simplify2.9s

Counts

122 → 122

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	168	1793
1	335	1679
2	1032	1425
3	2855	1415
done	5001	1415

prune586.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes212.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	18	26
done	18	26

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.4s	2506×	body	1280	valid
1.1s	8018×	body	80	valid
1.1s	2078×	body	640	valid
1.0s	1038×	body	320	valid
128.0ms	586×	body	160	valid