Details

sample221.0ms

Algorithm

intervals

Results

80.0ms	104×	body	1280	valid
49.0ms	268×	body	80	valid
37.0ms	71×	body	640	valid
11.0ms	28×	body	320	valid
6.0ms	22×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	49	13
3	76	13
4	95	13
5	111	13
6	126	13
7	142	13
done	142	13

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative`

Counts

3 → 98

Calls

3 calls:

14.0ms	(+ (* a1 a1) (* a2 a2))
43.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
11.0ms	(/ (cos th) (sqrt 2.0))

series466.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* a1 a1) (* a2 a2))
338.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
76.0ms	(/ (cos th) (sqrt 2.0))

simplify2.1s

Counts

107 → 107

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	158	1536
1	533	1481
2	3160	1327
done	5000	1322

prune485.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 94

Calls

3 calls:

12.0ms	(+ (* a1 a1) (* a2 a2))
40.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
62.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series481.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* a1 a1) (* a2 a2))
310.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
119.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify3.1s

Counts

103 → 103

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	141	1776
1	384	1691
2	2905	1549
done	5001	1547

prune394.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.3b	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
102×	`sqrt-prod`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt` `*-un-lft-identity`
78×	`cbrt-prod`
58×	`associate-r`
38×	`add-exp-log`
29×	`add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sqrt-div` `associate-/l*`
4×	`add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-*l/` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 201

Calls

4 calls:

30.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
232.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
14.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
26.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

398.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
219.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
56.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
43.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify564.0ms

Counts

213 → 213

Iterations

Useful iterations: done (553.0ms)

Iter	Nodes	Cost
0	256	6022
1	754	5475
done	5000	4997

prune891.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (+ (* a2 a2) (* a1 a1))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
0.5b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
4.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.3b	(sqrt (+ (* a2 a2) (* a1 a1)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
72×	`times-frac`
61×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
40×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`sqrt-div`
6×	`associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`sqrt-undiv` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 157

Calls

4 calls:

109.0ms	(* (* (sqrt (+ (* a2 a2) (* a1 a1))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
30.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
16.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
16.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(* (* (sqrt (+ (* a2 a2) (* a1 a1))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
165.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
63.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
69.0ms	(sqrt (+ (* a2 a2) (* a1 a1)))

simplify4.3s

Counts

169 → 169

Iterations

Useful iterations: 2 (738.0ms)

Iter	Nodes	Cost
0	215	3737
1	585	3345
2	4117	2895
done	5001	2895

prune751.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes254.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	19	32
done	19	32

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.6s	2619×	body	1280	valid
1.1s	8078×	body	80	valid
1.0s	2051×	body	640	valid
838.0ms	1001×	body	320	valid
106.0ms	507×	body	160	valid