Details

sample161.0ms

Algorithm

intervals

Results

54.0ms	82×	body	1280	valid
35.0ms	74×	body	640	valid
28.0ms	268×	body	80	valid
13.0ms	39×	body	320	valid
4.0ms	16×	body	160	valid

simplify337.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.4b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
16.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
18.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series561.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(fma a1 a1 (* a2 a2))
147.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
345.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.5s

Counts

70 → 70

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	103	947
1	201	911
2	750	777
3	3465	759
done	5000	758

prune310.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.4b	(* (cos th) (fma a1 a1 (* a2 a2)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
38.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
38.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
16.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma a1 a1 (* a2 a2))
1.0s	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
354.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
206.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

simplify1.2s

Counts

149 → 149

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	215	3852
1	473	3514
2	1765	3026
done	5000	3009

prune584.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.2b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
7.3b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
56×	`times-frac`
40×	`add-cbrt-cube`
36×	`cbrt-prod` `add-sqr-sqrt`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`pow1` `associate-/r*`
6×	`associate-r` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `fma-udef` `hypot-def` `associate-/l/`

Counts

4 → 152

Calls

4 calls:

25.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
46.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
54.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
3.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

292.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
1.1s	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
460.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
88.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify1.4s

Counts

164 → 164

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	236	5165
1	541	4599
2	2169	3146
done	5001	3123

prune671.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

224×	`times-frac`
83×	`add-sqr-sqrt`
81×	`add-cube-cbrt` `*-un-lft-identity`
78×	`cbrt-prod`
61×	`add-exp-log`
44×	`add-cbrt-cube`
39×	`sqrt-prod`
29×	`cbrt-undiv` `div-exp`
25×	`div-inv`
19×	`associate-/r*`
14×	`associate-/l*`
12×	`prod-exp` `cbrt-unprod`
11×	`associate-/r/`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num`
1×	`pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 239

Calls

4 calls:

18.0ms	(* (cos th) (hypot a1 a2))
19.0ms	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))
25.0ms	(/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))
53.0ms	(/ (/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (cbrt (sqrt 2.0)))

series2.2s

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (cos th) (hypot a1 a2))
466.0ms	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))
1.2s	(/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))
394.0ms	(/ (/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (cbrt (sqrt 2.0)))

simplify2.3s

Counts

251 → 251

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	356	7160
1	854	6864
2	3112	6090
done	5001	5891

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes334.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	18	33
done	18	33

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.3s	2498×	body	1280	valid
1.7s	1995×	body	640	valid
1.0s	8073×	body	80	valid
535.0ms	1075×	body	320	valid
179.0ms	529×	body	160	valid