Details

Time bar (total: 26.7s)

sample175.0ms

Algorithm
intervals
Results
80.0ms84×body1280valid
27.0ms67×body640valid
24.0ms255×body80valid
10.0ms30×body320valid
4.0ms20×body160valid

simplify139.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612613
714213
done14213

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite462.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
32×add-cbrt-cube add-exp-log
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 168
Calls
4 calls:
29.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
27.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
9.0ms
(/ (cos th) (sqrt 2.0))
385.0ms
(/ (cos th) (sqrt 2.0))

series491.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
139.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
85.0ms
(/ (cos th) (sqrt 2.0))
109.0ms
(/ (cos th) (sqrt 2.0))

simplify1.9s

Counts
180 → 180
Iterations

Useful iterations: 2 (677.0ms)

IterNodesCost
01812118
15412012
228731832
done50011832

prune985.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
345×add-sqr-sqrt
340×*-un-lft-identity add-cube-cbrt
37×associate-/l*
25×add-cbrt-cube add-exp-log
24×associate-/r*
22×associate-*l*
14×div-inv
9×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
4×add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 469
Calls
4 calls:
49.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
10.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
29.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
21.0ms
(/ (cos th) (sqrt 2.0))

series431.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
123.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
67.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
92.0ms
(/ (cos th) (sqrt 2.0))

simplify601.0ms

Counts
481 → 481
Iterations

Useful iterations: done (568.0ms)

IterNodesCost
04779858
111618538
done50008018

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
1143×sqrt-prod
1125×times-frac
615×add-sqr-sqrt
581×*-un-lft-identity add-cube-cbrt
283×associate-*l*
41×add-cbrt-cube add-exp-log
35×associate-/l*
24×associate-/r*
23×div-inv
13×cbrt-undiv div-exp unswap-sqr
12×prod-exp cbrt-unprod
9×pow1
4×add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 734
Calls
4 calls:
146.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
19.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
16.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
37.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
128.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
133.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
96.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.0s

Counts
746 → 746
Iterations

Useful iterations: done (977.0ms)

IterNodesCost
058414696
1177013025
done500112123

prune4.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
0.2b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
0.3b
(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite536.0ms

Algorithm
rewrite-expression-head
Rules
1440×sqrt-prod
975×times-frac
517×add-sqr-sqrt
515×associate-*l*
510×*-un-lft-identity add-cube-cbrt
142×add-exp-log
96×add-cbrt-cube
64×prod-exp
46×div-exp
42×cbrt-unprod
27×cbrt-undiv
18×pow1
16×div-inv
15×associate-/r*
9×pow-prod-down
5×rec-exp 1-exp
4×associate-*l/ associate-/l* add-log-exp unswap-sqr
2×clear-num frac-2neg associate-*r* *-commutative
1×frac-times associate-*r/
Counts
4 → 674
Calls
4 calls:
61.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
318.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
37.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
18.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series703.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2))
158.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a2 a2)))
177.0ms
(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
147.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify846.0ms

Counts
686 → 686
Iterations

Useful iterations: done (807.0ms)

IterNodesCost
056115583
1179114234
done500112984

prune4.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes580.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01429
11729
done1729

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.3s2548×body1280valid
1.5s2150×body640valid
1.1s8045×body80valid
445.0ms970×body320valid
116.0ms558×body160valid