Details

sample123.0ms

Algorithm

intervals

Results

44.0ms	85×	body	1280	valid
21.0ms	260×	body	80	valid
20.0ms	54×	body	640	valid
8.0ms	30×	body	320	valid
2.0ms	15×	body	160	valid

simplify160.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.6b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite90.0ms

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))
59.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
19.0ms	(/ (cos th) (sqrt 2.0))

series403.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (* a1 a1) (* a2 a2))
300.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
68.0ms	(/ (cos th) (sqrt 2.0))

simplify2.0s

Counts

107 → 107

Iterations

Useful iterations: done (2.0s)

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

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.6b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite365.0ms

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:

10.0ms	(+ (* a1 a1) (* a2 a2))
190.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
41.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
18.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* a1 a1) (* a2 a2))
279.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
74.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
132.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify1.0s

Counts

729 → 729

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	553	15882
1	2052	14258
done	5000	13378

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
0.6b	(* (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite815.0ms

Algorithm

rewrite-expression-head

Rules

1588×	`times-frac`
1571×	`sqrt-prod`
987×	`add-sqr-sqrt`
786×	`*-un-lft-identity`
762×	`add-cube-cbrt`
406×	`cbrt-prod`
379×	`associate-r`
99×	`add-exp-log`
61×	`add-cbrt-cube`
58×	`unswap-sqr`
42×	`div-exp`
34×	`associate-/l*`
31×	`prod-exp`
29×	`div-inv`
22×	`cbrt-undiv`
21×	`associate-/r*`
19×	`cbrt-unprod`
15×	`pow1`
14×	`associate-l`
10×	`frac-times`
7×	`pow-flip` `sqrt-pow1` `associate-*l/`
6×	`rec-exp` `1-exp` `associate-*r/`
4×	`flip3-+` `pow-prod-down` `flip-+` `add-log-exp`
3×	`pow1/2`
2×	`frac-2neg` `pow1/3` `clear-num` `*-commutative` `pow-div`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/` `inv-pow`

Counts

4 → 1013

Calls

4 calls:

240.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
274.0ms	(* (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
55.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
19.0ms	(/ 1 (sqrt (sqrt 2.0)))

series2.0s

Counts

4 → 8

Calls

4 calls:

679.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
1.4s	(* (* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify2.8s

Counts

1021 → 1021

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	920	25355
1	3361	20832
done	5000	19933

prune2.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (pow a1 2) (cos th)) (fabs (cbrt (sqrt 2.0))))
0.2b	(/ (* (cos th) (pow a2 2)) (fabs (cbrt (sqrt 2.0))))
0.3b	(* (pow a1 2) (cos th))
0.4b	(* (cbrt (/ 1 2.0)) (+ (/ (* (pow a1 2) (cos th)) (fabs (cbrt (sqrt 2.0)))) (/ (* (cos th) (pow a2 2)) (fabs (cbrt (sqrt 2.0))))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
31×	`add-exp-log`
24×	`associate-l`
23×	`*-un-lft-identity`
20×	`add-cube-cbrt`
17×	`times-frac` `add-cbrt-cube`
16×	`cbrt-prod`
10×	`prod-exp`
8×	`div-exp` `associate-r` `unswap-sqr`
6×	`pow1` `associate-/r*`
5×	`div-inv`
4×	`cbrt-undiv` `unpow-prod-down` `cbrt-div` `cbrt-unprod` `add-log-exp`
3×	`frac-times` `pow-to-exp` `associate-*r/` `pow-exp`
2×	`frac-2neg` `flip3-+` `frac-add` `clear-num` `-commutative` `flip-+` `associate-/l` `unpow2` `sqr-pow`
1×	`distribute-rgt-in` `distribute-rgt-out` `distribute-lft-in` `pow-prod-down` `associate-*l/` `distribute-lft-out`

Counts

4 → 118

Calls

4 calls:

27.0ms	(/ (* (pow a1 2) (cos th)) (fabs (cbrt (sqrt 2.0))))
23.0ms	(/ (* (cos th) (pow a2 2)) (fabs (cbrt (sqrt 2.0))))
15.0ms	(* (pow a1 2) (cos th))
113.0ms	(* (cbrt (/ 1 2.0)) (+ (/ (* (pow a1 2) (cos th)) (fabs (cbrt (sqrt 2.0)))) (/ (* (cos th) (pow a2 2)) (fabs (cbrt (sqrt 2.0))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

244.0ms	(/ (* (pow a1 2) (cos th)) (fabs (cbrt (sqrt 2.0))))
295.0ms	(/ (* (cos th) (pow a2 2)) (fabs (cbrt (sqrt 2.0))))
64.0ms	(* (pow a1 2) (cos th))
766.0ms	(* (cbrt (/ 1 2.0)) (+ (/ (* (pow a1 2) (cos th)) (fabs (cbrt (sqrt 2.0)))) (/ (* (cos th) (pow a2 2)) (fabs (cbrt (sqrt 2.0))))))

simplify2.5s

Counts

130 → 130

Iterations

Useful iterations: 2 (582.0ms)

Iter	Nodes	Cost
0	244	2857
1	705	2713
2	4222	2476
done	5000	2476

prune779.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes397.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	22	32
1	29	30
2	31	28
3	35	28
4	37	28
done	37	28

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.0s	2091×	body	640	valid
1.8s	2490×	body	1280	valid
1.4s	8065×	body	80	valid
457.0ms	1047×	body	320	valid
111.0ms	555×	body	160	valid