Details

sample90.0ms

Algorithm

intervals

Results

27.0ms	88×	body	1280	valid
17.0ms	263×	body	80	valid
16.0ms	77×	body	640	valid
6.0ms	39×	body	320	valid
2.0ms	17×	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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

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:

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

series286.0ms

Counts

2 → 6

Calls

2 calls:

227.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
59.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	479	795
1	2384	738
2	5002	725
done	5002	725

prune249.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 83

Calls

2 calls:

32.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
28.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series323.0ms

Counts

2 → 6

Calls

2 calls:

224.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
98.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify45.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	314	880
1	1523	816
2	5002	800
done	5002	800

prune215.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.3b	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
7.0b	(sqrt (+ (* a1 a1) (* a2 a2)))
7.0b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
102×	`sqrt-prod`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt` `*-un-lft-identity`
78×	`cbrt-prod`
58×	`associate-r`
38×	`add-exp-log`
29×	`add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sqrt-div` `associate-/l*`
4×	`add-log-exp`
3×	`flip3-+` `associate-*r/` `pow-prod-down` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-l` `associate-l/` `clear-num` `-commutative`

Counts

4 → 201

Calls

4 calls:

18.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
136.0ms	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
8.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
8.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
228.0ms	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
43.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
39.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify114.0ms

Counts

213 → 213

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	703	3560
1	3971	3228
2	5001	3067
done	5001	3067

prune603.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0)))))
0.4b	(/ (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
7.0b	(sqrt (+ (* a1 a1) (* a2 a2)))
7.0b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

129×	`add-exp-log`
100×	`cbrt-prod`
84×	`add-sqr-sqrt` `add-cbrt-cube`
82×	`times-frac`
76×	`associate-r`
66×	`sqrt-prod`
56×	`add-cube-cbrt` `*-un-lft-identity`
54×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
9×	`unswap-sqr`
8×	`pow1`
5×	`associate-l`
4×	`sqrt-div` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 198

Calls

4 calls:

183.0ms	(* (/ (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0)))))
41.0ms	(/ (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
11.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
8.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

234.0ms	(* (/ (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0)))))
707.0ms	(/ (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
37.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
39.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify68.0ms

Counts

210 → 210

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1066	6252
1	5001	5247
done	5001	5247

prune716.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes162.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7
done	13	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

810.0ms	2550×	body	1280	valid
446.0ms	2099×	body	640	valid
419.0ms	8227×	body	80	valid
168.0ms	1059×	body	320	valid
54.0ms	494×	body	160	valid