Details

Time bar (total: 9.4s)

sample73.0ms

Algorithm
intervals
Results
20.0ms63×body1280valid
17.0ms74×body640valid
16.0ms278×body80valid
3.0ms21×body320valid
2.0ms21×body160valid

simplify61.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24513
36513
48413
510213
611513
done11513

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

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))

rewrite32.0ms

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:
3.0ms
(+ (* a1 a1) (* a2 a2))
21.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms
(/ (cos th) (sqrt 2.0))

series307.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* a1 a1) (* a2 a2))
221.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
58.0ms
(/ (cos th) (sqrt 2.0))

simplify773.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (161.0ms)

IterNodesCost
01581536
14941477
221871319
done50001319

prune287.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.2b
(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.4b
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite21.0ms

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:
3.0ms
(+ (* a1 a1) (* a2 a2))
10.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
7.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series364.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* a1 a1) (* a2 a2))
117.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
219.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify694.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
01151083
13131042
21498882
done5000882

prune200.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
0.4b
(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
6.3b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.3b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×sqrt-div
16×sqrt-prod
15×add-exp-log add-cbrt-cube
13×add-cube-cbrt *-un-lft-identity
10×associate-*r/
9×flip3-+ flip-+
8×pow1 associate-/l/
6×times-frac associate-*r* associate-/r*
4×frac-times prod-exp cbrt-unprod add-log-exp
3×cbrt-undiv div-exp associate-*l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ unswap-sqr
1×frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 91
Calls
4 calls:
11.0ms
(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
23.0ms
(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
212.0ms
(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
35.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
40.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify568.0ms

Counts
103 → 103
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
01401989
13431535
215501317
done50011317

prune339.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize12.0ms

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)))

rewrite199.0ms

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:
3.0ms
(+ (* a1 a1) (* a2 a2))
109.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
19.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* a1 a1) (* a2 a2))
215.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
99.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify569.0ms

Counts
729 → 729
Iterations

Useful iterations: done (540.0ms)

IterNodesCost
055315882
1196814573
done500014196

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes231.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: done (2.0ms)

IterNodesCost
01627
12225
done2223

end0.0ms

sample2.2s

Algorithm
intervals
Results
791.0ms2478×body1280valid
476.0ms2138×body640valid
404.0ms7988×body80valid
158.0ms1016×body320valid
64.0ms545×body160valid