Details

sample145.0ms

Algorithm

intervals

Results

41.0ms	64×	body	1280	valid
35.0ms	79×	body	640	valid
24.0ms	245×	body	80	valid
9.0ms	27×	body	320	valid
5.0ms	21×	body	160	valid

simplify213.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

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))

rewrite97.0ms

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:

12.0ms	(+ (* a1 a1) (* a2 a2))
50.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
28.0ms	(/ (cos th) (sqrt 2.0))

series407.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(+ (* a1 a1) (* a2 a2))
264.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
88.0ms	(/ (cos th) (sqrt 2.0))

simplify2.1s

Counts

107 → 107

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	158	1536
1	480	1469
2	1599	1325
done	5000	1322

prune414.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

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))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite348.0ms

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))
156.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
59.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
12.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* a1 a1) (* a2 a2))
350.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
78.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
171.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify1.6s

Counts

729 → 729

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	553	15882
1	1946	14258
done	5000	13265

prune2.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite649.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 648

Calls

4 calls:

8.0ms	(+ (* a2 a2) (* a1 a1))
64.0ms	(* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt (sqrt 2.0))))
421.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt (sqrt 2.0)))))
24.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series807.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a2 a2) (* a1 a1))
355.0ms	(* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt (sqrt 2.0))))
278.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (+ (* a2 a2) (* a1 a1)) (/ (cos th) (sqrt (sqrt 2.0)))))
141.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify2.8s

Counts

660 → 660

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	531	17479
1	1567	16051
2	4713	14217
done	5000	13905

prune3.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
5.9b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.9b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

600×	`sqrt-prod`
576×	`times-frac`
316×	`add-sqr-sqrt`
314×	`add-cube-cbrt` `*-un-lft-identity`
34×	`associate-/l*`
18×	`associate-/r*`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `flip-+`
1×	`associate-/l/`

Counts

4 → 415

Calls

4 calls:

60.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
37.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
17.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
149.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
45.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
66.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify2.9s

Counts

427 → 427

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	428	9225
1	945	7904
2	1752	7361
3	3990	7177
done	5000	7114

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes311.0ms

Accuracy

0% (0.3b 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

2.2s	2506×	body	1280	valid
1.7s	8018×	body	80	valid
1.3s	2078×	body	640	valid
367.0ms	1038×	body	320	valid
131.0ms	586×	body	160	valid