Details

sample85.0ms

Algorithm

intervals

Results

26.0ms	84×	body	1280	valid
18.0ms	66×	body	640	valid
12.0ms	247×	body	80	valid
6.0ms	39×	body	320	valid
2.0ms	21×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7
done	141	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

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))

rewrite61.0ms

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:

8.0ms	(+ (* a1 a1) (* a2 a2))
40.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
10.0ms	(/ (cos th) (sqrt 2.0))

series317.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* a1 a1) (* a2 a2))
222.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify53.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5003	791
done	5003	791

prune307.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 717

Calls

4 calls:

8.0ms	(+ (* a1 a1) (* a2 a2))
129.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
12.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
32.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* a1 a1) (* a2 a2))
221.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
100.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
69.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify103.0ms

Counts

729 → 729

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573
done	5001	9573

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.3b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

1434×	`sqrt-prod`
969×	`times-frac`
518×	`add-sqr-sqrt`
515×	`associate-l`
507×	`add-cube-cbrt` `*-un-lft-identity`
71×	`add-exp-log`
47×	`add-cbrt-cube`
27×	`prod-exp`
25×	`div-exp`
17×	`cbrt-unprod`
15×	`div-inv`
14×	`cbrt-undiv`
11×	`pow1` `frac-times` `associate-*r/`
9×	`associate-/r*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `associate-*l/` `unswap-sqr`
3×	`rec-exp` `1-exp` `associate-/l*`
2×	`*-commutative`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 654

Calls

4 calls:

9.0ms	(+ (* a1 a1) (* a2 a2))
42.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
239.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
14.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series648.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* a1 a1) (* a2 a2))
298.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
220.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
98.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify106.0ms

Counts

666 → 666

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1788	11355
1	5001	10426
done	5001	10426

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))) (sqrt (sqrt (sqrt 2.0))))
0.3b	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
0.3b	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

156×	`sqrt-prod`
105×	`times-frac`
103×	`add-exp-log`
90×	`add-sqr-sqrt`
79×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-l`
61×	`add-cbrt-cube`
42×	`prod-exp`
35×	`div-exp`
22×	`cbrt-unprod`
21×	`associate-/r*`
20×	`frac-times` `associate-*r/`
19×	`cbrt-undiv`
11×	`pow1` `associate-/l/`
10×	`flip3-+` `flip-+`
7×	`associate-*l/`
6×	`rec-exp` `1-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `div-inv` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 259

Calls

4 calls:

86.0ms	(/ (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))) (sqrt (sqrt (sqrt 2.0))))
93.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
44.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
11.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))) (sqrt (sqrt (sqrt 2.0))))
711.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
306.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
100.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify61.0ms

Counts

271 → 271

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1144	3957
1	5001	3367
done	5001	3367

prune784.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes233.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.3s

Algorithm

intervals

Results

791.0ms	2508×	body	1280	valid
459.0ms	2129×	body	640	valid
400.0ms	7960×	body	80	valid
163.0ms	1074×	body	320	valid
49.0ms	478×	body	160	valid