Details

Time bar (total: 11.1s)

sample80.0ms

Algorithm
intervals
Results
31.0ms88×body1280valid
14.0ms67×body640valid
13.0ms246×body80valid
5.0ms35×body320valid
2.0ms15×body160valid

simplify95.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01219
12613
25212
37512
410212
512212
613912
714312
814512
done14512

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.5b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 176
Calls
4 calls:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series343.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
113.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
63.0ms
(/ (cos th) (sqrt 2.0))
58.0ms
(/ (cos th) (sqrt 2.0))

simplify560.0ms

Counts
188 → 188
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
01872182
14982076
216101874
done50001874

prune506.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b
(* (/ (cos th) (sqrt 2.0)) a2)
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
74×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
25×add-exp-log add-cbrt-cube
12×associate-/r*
11×pow1
8×prod-exp cbrt-unprod
6×associate-/l* unswap-sqr
5×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*l/ clear-num *-commutative
Counts
4 → 173
Calls
4 calls:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
12.0ms
(* (/ (cos th) (sqrt 2.0)) a2)
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series529.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
297.0ms
(* (/ (cos th) (sqrt 2.0)) a2)
63.0ms
(/ (cos th) (sqrt 2.0))
62.0ms
(/ (cos th) (sqrt 2.0))

simplify538.0ms

Counts
185 → 185
Iterations

Useful iterations: 2 (160.0ms)

IterNodesCost
01812019
14441920
213811762
done50001762

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos th) (/ a2 (sqrt 2.0))) a2)
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b
(/ a2 (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
53×add-sqr-sqrt
48×add-cube-cbrt *-un-lft-identity
34×sqrt-prod
29×add-exp-log add-cbrt-cube
23×associate-*l*
14×pow1
12×associate-/r*
11×prod-exp cbrt-unprod
6×pow-prod-down associate-/l*
5×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×div-inv unswap-sqr
2×frac-2neg associate-*l/ clear-num *-commutative
1×associate-*r/
Counts
4 → 152
Calls
4 calls:
18.0ms
(* (* (cos th) (/ a2 (sqrt 2.0))) a2)
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
3.0ms
(/ a2 (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series327.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (* (cos th) (/ a2 (sqrt 2.0))) a2)
106.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
54.0ms
(/ a2 (sqrt 2.0))
59.0ms
(/ (cos th) (sqrt 2.0))

simplify596.0ms

Counts
164 → 164
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
02191814
15141712
217451530
done50011530

prune413.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.4b
(/ a2 (sqrt 2.0))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
24×associate-/r*
23×div-inv
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 752
Calls
4 calls:
94.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
5.0ms
(/ a2 (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
57.0ms
(/ a2 (sqrt 2.0))
97.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
67.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.6s

Counts
764 → 764
Iterations

Useful iterations: done (1.6s)

IterNodesCost
058614710
1157213016
2408612022
done500112020

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes320.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01830
12330
done2330

end0.0ms

sample2.3s

Algorithm
intervals
Results
825.0ms2539×body1280valid
482.0ms2251×body640valid
399.0ms8054×body80valid
167.0ms1053×body320valid
52.0ms473×body160valid