Details

Time bar (total: 1.9m)

sample502.0ms

Algorithm
intervals
Results
103.0ms256×body80valid
20.0ms256×pre80true

simplify10.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
27119
315519
447219
5316119
done500019

prune264.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize172.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite940.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l* prod-exp add-cbrt-cube
12×pow1
11×times-frac
8×associate-*r*
6×pow-exp add-log-exp
5×cbrt-unprod
4×div-exp pow-prod-down unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative flip3-+ associate-*l/ sum-log flip-+ div-inv
Counts
4 → 87
Calls
4 calls:
213.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
382.0ms
(pow (* -2.0 (log u1)) 0.5)
82.0ms
(* (* 2.0 PI) u2)
225.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series8.6s

Counts
4 → 12
Calls
4 calls:
3.3s
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
1.2s
(pow (* -2.0 (log u1)) 0.5)
145.0ms
(* (* 2.0 PI) u2)
4.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify9.5s

Counts
99 → 99
Iterations

Useful iterations: done (9.3s)

IterNodesCost
02031408
15471350
225481230
done50001207

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize537.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.3b
(* (* 2.0 PI) u2)

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
14×add-cbrt-cube
12×pow1
9×prod-exp
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×div-exp
4×pow-prod-down pow-exp cbrt-unprod
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×+-commutative unpow-prod-down frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv associate-/l* sqr-pow
Counts
4 → 70
Calls
4 calls:
219.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
15.0ms
(pow (* -2.0 (log u1)) 0.5)
78.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
102.0ms
(* (* 2.0 PI) u2)

series10.3s

Counts
4 → 12
Calls
4 calls:
3.7s
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
1.3s
(pow (* -2.0 (log u1)) 0.5)
4.9s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
329.0ms
(* (* 2.0 PI) u2)

simplify9.2s

Counts
82 → 82
Iterations

Useful iterations: done (9.0s)

IterNodesCost
01841168
15161127
22465996
done5000983

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite641.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log add-sqr-sqrt
33×associate-*l*
30×sqrt-prod
23×add-cube-cbrt *-un-lft-identity
20×times-frac
19×prod-exp
16×add-cbrt-cube
14×pow1
9×associate-*r*
7×cbrt-unprod
6×pow-exp unswap-sqr
5×sqrt-div pow-prod-down sqr-pow
4×associate-*l/ add-log-exp
3×pow-to-exp pow-unpow *-commutative
2×unpow-prod-down pow-pow div-inv
1×frac-times associate-*r/
Counts
4 → 112
Calls
4 calls:
12.0ms
(pow (* -2.0 (log u1)) 0.5)
324.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
197.0ms
(* (* 2.0 PI) u2)
67.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series12.1s

Counts
4 → 12
Calls
4 calls:
1.1s
(pow (* -2.0 (log u1)) 0.5)
5.5s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
115.0ms
(* (* 2.0 PI) u2)
5.3s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify9.8s

Counts
124 → 124
Iterations

Useful iterations: done (9.6s)

IterNodesCost
02001773
14851686
221321442
done50001413

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize149.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

rewrite388.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
36×times-frac
32×div-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity prod-exp
23×add-cbrt-cube
13×pow1
10×pow-exp
8×associate-/r*
7×cbrt-undiv
6×rec-exp 1-exp div-inv associate-/l*
5×pow-to-exp cbrt-unprod
4×pow-prod-down add-log-exp
3×pow-unpow associate-*r*
2×pow-pow frac-2neg clear-num
1×unpow-prod-down pow-flip associate-*l* associate-/r/ *-commutative inv-pow sqr-pow
Counts
4 → 124
Calls
4 calls:
21.0ms
(pow (* -2.0 (log u1)) 0.5)
56.0ms
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
35.0ms
(* (* 2.0 PI) u2)
215.0ms
(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

series8.5s

Counts
4 → 12
Calls
4 calls:
1.2s
(pow (* -2.0 (log u1)) 0.5)
4.0s
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
120.0ms
(* (* 2.0 PI) u2)
3.2s
(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

simplify6.6s

Counts
136 → 136
Iterations

Useful iterations: done (6.5s)

IterNodesCost
02301910
16061726
229841557
done50001545

prune2.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes2.3s

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify30.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
02025
12725
done2725

end0.0ms

sample9.6s

Algorithm
intervals
Results
6.9s8000×body80valid
2.2s8000×pre80true