Details

Time bar (total: 18.4s)

sample336.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
4.0ms256×pre80true

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
27119
315219
444019
5138519
done500019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

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)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite109.0ms

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:
58.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
17.0ms
(* (* 2.0 PI) u2)
24.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts
4 → 12
Calls
4 calls:
490.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
273.0ms
(pow (* -2.0 (log u1)) 0.5)
40.0ms
(* (* 2.0 PI) u2)
733.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify974.0ms

Counts
99 → 99
Iterations

Useful iterations: done (971.0ms)

IterNodesCost
02031408
14991344
216551222
done50001191

prune346.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize22.0ms

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

rewrite82.0ms

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:
48.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
9.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
17.0ms
(* (* 2.0 PI) u2)

series1.5s

Counts
4 → 12
Calls
4 calls:
469.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
271.0ms
(pow (* -2.0 (log u1)) 0.5)
704.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
34.0ms
(* (* 2.0 PI) u2)

simplify984.0ms

Counts
96 → 96
Iterations

Useful iterations: done (981.0ms)

IterNodesCost
01951363
14351318
213951206
done50011175

prune328.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ 0.5 (* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* 2.0 PI) u2)))))
0.1b
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5)
0.3b
(* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* 2.0 PI) u2))))
0.3b
(* (* 2.0 PI) u2)

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
66×prod-exp
48×pow-exp
21×pow-to-exp
14×add-cbrt-cube
10×pow1
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate-*l* cbrt-unprod add-log-exp
4×associate-*r* pow-prod-down
3×pow-unpow
2×unpow-prod-down pow-pow *-commutative sqr-pow
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 94
Calls
4 calls:
12.0ms
(+ 0.5 (* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* 2.0 PI) u2)))))
17.0ms
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5)
71.0ms
(* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* 2.0 PI) u2))))
17.0ms
(* (* 2.0 PI) u2)

series1.8s

Counts
4 → 12
Calls
4 calls:
467.0ms
(+ 0.5 (* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* 2.0 PI) u2)))))
886.0ms
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5)
457.0ms
(* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) (* 0.16666666666666666 (cos (* (* 2.0 PI) u2))))
38.0ms
(* (* 2.0 PI) u2)

simplify1.1s

Counts
106 → 106
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02162279
15371917
216071760
done50001739

prune288.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
38×log-prod
34×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
26×add-exp-log
19×exp-sum
11×pow1 add-cbrt-cube
10×unpow-prod-down sqr-pow
8×div-exp
5×rem-log-exp prod-exp associate-/l*
4×exp-prod pow-exp add-log-exp
3×associate-*r* pow-prod-down associate-/r* cbrt-unprod div-inv
2×pow-to-exp log-div log-pow
1×cbrt-undiv frac-2neg exp-diff associate-*l* clear-num *-commutative rem-exp-log
Counts
4 → 121
Calls
4 calls:
4.0ms
(log (/ (pow (* -2.0 (log u1)) 0.5) 6.0))
8.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
18.0ms
(* (* 2.0 PI) u2)
6.0ms
(exp (log (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))

series2.2s

Counts
4 → 12
Calls
4 calls:
819.0ms
(log (/ (pow (* -2.0 (log u1)) 0.5) 6.0))
699.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
33.0ms
(* (* 2.0 PI) u2)
680.0ms
(exp (log (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))

simplify2.0s

Counts
133 → 133
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02291946
14201787
211781670
342581610
done50001604

prune482.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes393.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02123
12821
done2821

end0.0ms

sample944.0ms

Algorithm
intervals
Results
633.0ms8000×body80valid
114.0ms8000×pre80true