Details

sample145.0ms

Algorithm

intervals

Results

61.0ms	84×	body	1280	valid
22.0ms	69×	body	640	valid
19.0ms	237×	body	80	valid
9.0ms	35×	body	320	valid
4.0ms	25×	body	160	valid

simplify233.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	49	13
3	76	13
4	95	13
5	111	13
6	125	13
7	139	13
done	139	13

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 87

Calls

2 calls:

57.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
22.0ms	(/ (cos th) (sqrt 2.0))

series384.0ms

Counts

2 → 6

Calls

2 calls:

307.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
77.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	153	1370
1	471	1308
2	1592	1194
done	5000	1191

prune394.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite383.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
624×	`add-sqr-sqrt`
577×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
34×	`associate-/l*`
22×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`associate-r` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

3 → 706

Calls

3 calls:

210.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
70.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
25.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series624.0ms

Counts

3 → 9

Calls

3 calls:

357.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
115.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
151.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify1.5s

Counts

715 → 715

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	548	15716
1	1937	14097
done	5001	13124

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.2b

(/ (cos th) (sqrt (sqrt (sqrt 2.0))))

0.2b

(/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

0.3b

(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

132×	`sqrt-prod`
82×	`times-frac`
75×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
40×	`associate-l`
31×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
6×	`associate-/l*`
5×	`pow1` `unswap-sqr`
4×	`div-inv`
3×	`add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

3 → 162

Calls

3 calls:

15.0ms

(/ (cos th) (sqrt (sqrt (sqrt 2.0))))

56.0ms

(/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

181.0ms

(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

series1.3s

Counts

3 → 9

Calls

3 calls:

344.0ms

(/ (cos th) (sqrt (sqrt (sqrt 2.0))))

618.0ms

(/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

320.0ms

(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

simplify1.5s

Counts

171 → 171

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	244	4018
1	598	3786
2	2371	2946
done	5000	2937

prune834.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (sqrt (sqrt 2.0))) (cos th))
0.2b	(/ 1 (/ (sqrt (sqrt (sqrt 2.0))) (cos th)))
0.2b	(/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(* (/ 1 (/ (sqrt (sqrt (sqrt 2.0))) (cos th))) (/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

552×	`times-frac`
462×	`sqrt-prod`
329×	`add-sqr-sqrt`
299×	`*-un-lft-identity`
294×	`add-cube-cbrt`
125×	`associate-l`
100×	`add-exp-log`
52×	`add-cbrt-cube`
45×	`div-exp`
44×	`associate-/r*`
29×	`prod-exp`
21×	`cbrt-undiv`
18×	`associate-/l*`
13×	`cbrt-unprod`
12×	`div-inv`
11×	`unswap-sqr`
8×	`rec-exp` `1-exp`
7×	`pow1` `associate-r`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/r/` `associate-/l/`
1×	`frac-times` `pow-flip` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 455

Calls

4 calls:

17.0ms	(/ (sqrt (sqrt (sqrt 2.0))) (cos th))
43.0ms	(/ 1 (/ (sqrt (sqrt (sqrt 2.0))) (cos th)))
46.0ms	(/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
180.0ms	(* (/ 1 (/ (sqrt (sqrt (sqrt 2.0))) (cos th))) (/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

304.0ms	(/ (sqrt (sqrt (sqrt 2.0))) (cos th))
350.0ms	(/ 1 (/ (sqrt (sqrt (sqrt 2.0))) (cos th)))
616.0ms	(/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
324.0ms	(* (/ 1 (/ (sqrt (sqrt (sqrt 2.0))) (cos th))) (/ (+ (* a2 a2) (* a1 a1)) (* (sqrt (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))))

simplify2.4s

Counts

467 → 467

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	492	11365
1	1294	9858
2	3861	7949
done	5000	7733

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes321.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	22	26
done	22	26

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.9s	2506×	body	1280	valid
1.7s	8004×	body	80	valid
1.6s	2088×	body	640	valid
317.0ms	1028×	body	320	valid
114.0ms	544×	body	160	valid