Details

sample147.0ms

Algorithm

intervals

Results

67.0ms	85×	body	1280	valid
22.0ms	66×	body	640	valid
20.0ms	259×	body	80	valid
10.0ms	39×	body	320	valid
2.0ms	13×	body	160	valid

simplify138.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

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))

rewrite117.0ms

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:

21.0ms	(+ (* a1 a1) (* a2 a2))
74.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
17.0ms	(/ (cos th) (sqrt 2.0))

series406.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* a1 a1) (* a2 a2))
306.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
64.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

107 → 107

Iterations

Useful iterations: done (1.7s)

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

prune524.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize15.0ms

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)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite360.0ms

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:

9.0ms	(+ (* a1 a1) (* a2 a2))
216.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
12.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
51.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a1 a1) (* a2 a2))
317.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
142.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
100.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.5s

Counts

729 → 729

Iterations

Useful iterations: done (1.4s)

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

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
0.4b	(* (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
0.7b	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

1548×	`sqrt-prod`
1171×	`times-frac`
1040×	`add-sqr-sqrt`
494×	`*-un-lft-identity`
434×	`add-cube-cbrt`
379×	`associate-r`
145×	`unswap-sqr`
92×	`add-exp-log`
58×	`add-cbrt-cube`
41×	`associate-l`
37×	`div-exp`
31×	`prod-exp`
21×	`associate-/r*`
20×	`cbrt-undiv`
19×	`cbrt-unprod`
16×	`div-inv`
14×	`pow1`
10×	`frac-times`
7×	`associate-*l/`
6×	`associate-r/` `associate-/l`
5×	`rec-exp` `pow-flip` `1-exp`
4×	`sqrt-pow1` `flip3-+` `pow-prod-down` `flip-+` `add-log-exp`
2×	`frac-2neg` `pow1/2` `clear-num` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `inv-pow`

Counts

4 → 756

Calls

4 calls:

14.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
382.0ms	(* (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
458.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
18.0ms	(/ 1 (sqrt (sqrt 2.0)))

series899.0ms

Counts

4 → 10

Calls

4 calls:

425.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
354.0ms	(* (* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
120.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify1.8s

Counts

766 → 766

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	767	19971
1	2404	17023
done	5000	15061

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.5b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

8.0ms	(+ (* a1 a1) (* a2 a2))
54.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
36.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series567.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* a1 a1) (* a2 a2))
163.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
352.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify1.6s

Counts

71 → 71

Iterations

Useful iterations: 2 (276.0ms)

Iter	Nodes	Cost
0	115	1083
1	303	1038
2	1190	886
done	5000	886

prune243.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes273.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.8s	2529×	body	1280	valid
1.1s	2128×	body	640	valid
1.1s	8050×	body	80	valid
888.0ms	1047×	body	320	valid
99.0ms	487×	body	160	valid