Details

Time bar (total: 7.3s)

sample85.0ms

Algorithm
intervals
Results
27.0ms89×body1280valid
15.0ms264×body80valid
15.0ms70×body640valid
6.0ms42×body320valid
2.0ms20×body160valid

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417
done1417

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

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))

rewrite61.0ms

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))
39.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
10.0ms
(/ (cos th) (sqrt 2.0))

series300.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* a1 a1) (* a2 a2))
211.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
61.0ms
(/ (cos th) (sqrt 2.0))

simplify53.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0490872
12426805
25003791
done5003791

prune286.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite55.0ms

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))
27.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
19.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series360.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* a1 a1) (* a2 a2))
112.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
212.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify43.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0309564
11642490
25001481
done5001481

prune185.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
0.7b
(/ (cos th) (sqrt 2.0))
6.5b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.5b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×times-frac
36×add-cube-cbrt *-un-lft-identity
35×sqrt-prod
22×associate-*l*
11×add-exp-log add-cbrt-cube
8×pow1 sqrt-div
6×associate-*r* associate-/r* unswap-sqr
4×flip3-+ flip-+ add-log-exp
3×associate-/l*
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 121
Calls
4 calls:
43.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
10.0ms
(/ (cos th) (sqrt 2.0))
8.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
9.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
61.0ms
(/ (cos th) (sqrt 2.0))
35.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
41.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify42.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03521093
112561042
250011028
done50011028

prune382.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize13.0ms

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)))

rewrite236.0ms

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))
127.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
31.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
12.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a1 a1) (* a2 a2))
215.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
64.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
100.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify102.0ms

Counts
729 → 729
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0196110436
150019573
done50019573

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes211.0ms

Accuracy

0% (0.5b 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)

IterNodesCost
01613
11613
done1613

end0.0ms

sample2.3s

Algorithm
intervals
Results
799.0ms2521×body1280valid
452.0ms2120×body640valid
388.0ms7985×body80valid
148.0ms1005×body320valid
56.0ms511×body160valid