Details

Time bar (total: 26.7s)

sample151.0ms

Algorithm
intervals
Results
49.0ms256×body80valid
9.0ms256×pre80true

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01819
13419
27119
315219
444019
5138519
done500019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite237.0ms

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:
120.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
13.0ms
(pow (* -2.0 (log u1)) 0.5)
36.0ms
(* (* 2.0 PI) u2)
60.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
700.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
443.0ms
(pow (* -2.0 (log u1)) 0.5)
67.0ms
(* (* 2.0 PI) u2)
995.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
99 → 99
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02031408
14991344
216551222
done50001191

prune505.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×times-frac
12×pow1
11×add-cbrt-cube
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×div-exp pow-prod-down pow-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv
Counts
4 → 84
Calls
4 calls:
91.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
7.0ms
(pow (* -2.0 (log u1)) 0.5)
19.0ms
(* (* 2.0 PI) u2)
11.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series2.3s

Counts
4 → 12
Calls
4 calls:
735.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
383.0ms
(pow (* -2.0 (log u1)) 0.5)
54.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify1.4s

Counts
96 → 96
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01951363
14351318
213941206
done50011175

prune495.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×pow1
20×add-cbrt-cube
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×times-frac
12×associate-*r*
11×prod-exp
10×pow-prod-down
9×cbrt-unprod
6×sqrt-prod
5×unpow-prod-down associate-/l* sqr-pow
4×div-exp pow-exp add-log-exp
3×pow-unpow associate-/r*
2×pow-to-exp pow-pow associate-*l* *-commutative
1×cbrt-undiv frac-2neg clear-num div-inv
Counts
4 → 100
Calls
4 calls:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
123.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
9.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
23.0ms
(* (* 2.0 PI) (sqrt u2))

series1.8s

Counts
4 → 12
Calls
4 calls:
462.0ms
(pow (* -2.0 (log u1)) 0.5)
72.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
1.1s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
124.0ms
(* (* 2.0 PI) (sqrt u2))

simplify2.3s

Counts
112 → 112
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02051359
14661186
214671068
done50001052

prune656.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(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))

rewrite203.0ms

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:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
127.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
29.0ms
(* (* 2.0 PI) u2)
27.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series3.1s

Counts
4 → 12
Calls
4 calls:
389.0ms
(pow (* -2.0 (log u1)) 0.5)
1.6s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
58.0ms
(* (* 2.0 PI) u2)
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.9s

Counts
124 → 124
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02001773
14421551
214271422
done50011413

prune641.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes495.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02025
12725
done2725

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.6s8000×body80valid
352.0ms8000×pre80true