Details

Time bar (total: 30.5s)

sample154.0ms

Algorithm
intervals
Results
53.0ms85×body1280valid
29.0ms66×body640valid
28.0ms259×body80valid
13.0ms39×body320valid
3.0ms13×body160valid

simplify237.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612513
713913
done13913

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

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×div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
39.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
42.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
21.0ms
(/ (cos th) (sqrt 2.0))
18.0ms
(/ (cos th) (sqrt 2.0))

series521.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
172.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
74.0ms
(/ (cos th) (sqrt 2.0))
103.0ms
(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts
180 → 180
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01812118
14662012
213901832
done50001812

prune841.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite392.0ms

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×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 744
Calls
4 calls:
191.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
23.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
62.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
18.0ms
(/ (cos th) (sqrt 2.0))

series535.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
137.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
100.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
109.0ms
(/ (cos th) (sqrt 2.0))

simplify2.3s

Counts
756 → 756
Iterations

Useful iterations: done (2.3s)

IterNodesCost
056014715
1150513041
2336712042
done500011754

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
1188×sqrt-prod
1152×times-frac
620×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
68×associate-/l*
36×associate-/r*
24×div-inv
18×add-exp-log add-cbrt-cube
8×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num add-log-exp
2×associate-/l/
Counts
4 → 770
Calls
4 calls:
12.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
13.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
34.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
42.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
147.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
117.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
110.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify2.7s

Counts
782 → 782
Iterations

Useful iterations: done (2.7s)

IterNodesCost
039317598
186015064
2155514042
3357313698
done500113572

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (cos th) (pow a2 2)) (sqrt (sqrt 2.0)))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* (cos th) (pow a2 2)) (sqrt (sqrt 2.0))))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite632.0ms

Algorithm
rewrite-expression-head
Rules
1519×sqrt-prod
1036×times-frac
635×add-sqr-sqrt
519×*-un-lft-identity
506×associate-*l*
503×add-cube-cbrt
133×add-exp-log
59×add-cbrt-cube
57×div-exp
49×prod-exp
41×unswap-sqr
20×cbrt-undiv
19×cbrt-unprod
18×div-inv
15×associate-/r*
14×associate-*r*
11×pow1
6×pow-to-exp pow-exp
5×rec-exp 1-exp
4×pow-prod-down associate-/l* add-log-exp
2×frac-2neg associate-*l/ clear-num *-commutative
1×frac-times associate-*r/
Counts
4 → 700
Calls
4 calls:
17.0ms
(/ (* (cos th) (pow a2 2)) (sqrt (sqrt 2.0)))
68.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
399.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* (cos th) (pow a2 2)) (sqrt (sqrt 2.0))))
22.0ms
(/ (cos th) (sqrt 2.0))

series660.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(/ (* (cos th) (pow a2 2)) (sqrt (sqrt 2.0)))
171.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
147.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (/ (* (cos th) (pow a2 2)) (sqrt (sqrt 2.0))))
91.0ms
(/ (cos th) (sqrt 2.0))

simplify2.6s

Counts
712 → 712
Iterations

Useful iterations: done (2.6s)

IterNodesCost
054916968
1161415546
2431812133
done500012029

prune3.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes453.0ms

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)

IterNodesCost
01429
11729
done1729

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.1s2128×body640valid
1.9s2529×body1280valid
1.2s8050×body80valid
508.0ms1047×body320valid
107.0ms487×body160valid