Details

Time bar (total: 27.6s)

sample201.0ms

Algorithm
intervals
Results
50.0ms256×body80valid
9.0ms256×pre80true

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01819
13419
27119
315219
444019
5138519
done500019

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

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)
0.1b
(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))

rewrite167.0ms

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:
60.0ms
(+ (* (* (/ 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)
46.0ms
(* (* 2.0 PI) u2)
44.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
723.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
438.0ms
(pow (* -2.0 (log u1)) 0.5)
43.0ms
(* (* 2.0 PI) u2)
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.5s

Counts
99 → 99
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02031408
14991344
216551222
done50001191

prune576.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize42.0ms

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

rewrite164.0ms

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:
8.0ms
(pow (* -2.0 (log u1)) 0.5)
97.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
32.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
22.0ms
(* (* 2.0 PI) u2)

series2.7s

Counts
4 → 12
Calls
4 calls:
417.0ms
(pow (* -2.0 (log u1)) 0.5)
1.2s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
1.0s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
39.0ms
(* (* 2.0 PI) u2)

simplify1.8s

Counts
124 → 124
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02001773
14421551
214191422
done50001413

prune673.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5)
0.2b
(* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666)
0.3b
(* (* 2.0 PI) u2)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
33×prod-exp
32×pow-exp
14×pow-to-exp
11×add-sqr-sqrt add-cbrt-cube
10×pow1
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l* add-log-exp
4×pow-prod-down cbrt-unprod
3×pow-unpow sqr-pow
2×unpow-prod-down pow-pow *-commutative unswap-sqr
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 85
Calls
4 calls:
51.0ms
(+ (* (* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2))) 0.5)
18.0ms
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5)
35.0ms
(* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666)
24.0ms
(* (* 2.0 PI) u2)

series3.5s

Counts
4 → 12
Calls
4 calls:
639.0ms
(+ (* (* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2))) 0.5)
1.8s
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5)
1.1s
(* (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666)
39.0ms
(* (* 2.0 PI) u2)

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02111771
15101505
215361392
done50011357

prune439.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 2.0 PI) u2)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (* 2 0.5)) (* 0.16666666666666666 0.16666666666666666))
0.4b
(/ (- (* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (* 2 0.5)) (* 0.16666666666666666 0.16666666666666666)) (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

rewrite647.0ms

Algorithm
rewrite-expression-head
Rules
80×add-exp-log
60×prod-exp
32×pow-exp
21×add-cbrt-cube
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
14×pow1 pow-to-exp
9×times-frac cbrt-unprod
7×associate-*r* associate-*l*
6×pow-prod-down
4×add-log-exp
3×associate-/r* *-commutative associate-/l*
2×flip3-- associate-/r/ flip-- associate-/l/ unswap-sqr sqr-pow
1×cbrt-undiv unpow-prod-down frac-2neg div-sub div-exp clear-num div-inv
Counts
4 → 110
Calls
4 calls:
26.0ms
(* (* 2.0 PI) u2)
19.0ms
(* (* 2.0 PI) u2)
34.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (* 2 0.5)) (* 0.16666666666666666 0.16666666666666666))
561.0ms
(/ (- (* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (* 2 0.5)) (* 0.16666666666666666 0.16666666666666666)) (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series2.3s

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* 2.0 PI) u2)
41.0ms
(* (* 2.0 PI) u2)
1.1s
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (* 2 0.5)) (* 0.16666666666666666 0.16666666666666666))
1.1s
(/ (- (* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (* 2 0.5)) (* 0.16666666666666666 0.16666666666666666)) (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify1.5s

Counts
122 → 122
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02614221
16783855
223343482
done50003380

prune780.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes525.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02123
12821
done2821

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.4s8000×body80valid
265.0ms8000×pre80true