Details

Time bar (total: 31.5s)

sample154.0ms

Algorithm
intervals
Results
50.0ms256×body80valid
9.0ms256×pre80true

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
27119
315519
447219
5316119
done500019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

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

rewrite152.0ms

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:
70.0ms
(+ (* (* (/ 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)
33.0ms
(* (* 2.0 PI) u2)
25.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
650.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
359.0ms
(pow (* -2.0 (log u1)) 0.5)
63.0ms
(* (* 2.0 PI) u2)
999.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.7s

Counts
99 → 99
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02031408
15471350
225481230
done50001207

prune499.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize40.0ms

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))

rewrite143.0ms

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:
6.0ms
(pow (* -2.0 (log u1)) 0.5)
83.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
17.0ms
(* (* 2.0 PI) u2)
33.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.6s

Counts
4 → 12
Calls
4 calls:
438.0ms
(pow (* -2.0 (log u1)) 0.5)
1.1s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
42.0ms
(* (* 2.0 PI) u2)
994.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.5s

Counts
124 → 124
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02001773
14851686
221321442
done50001413

prune744.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 2.0 PI) u2)
0.4b
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b
(/ (- (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
103×add-exp-log
54×prod-exp
34×add-cbrt-cube
31×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×div-exp
20×times-frac
15×associate-*l*
14×pow-exp cbrt-unprod
13×associate-*r*
9×pow1
7×pow-to-exp
6×cbrt-undiv unswap-sqr
5×associate-*l/ sqr-pow
4×add-log-exp
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×unpow-prod-down flip3-- associate-/r/ flip-- div-inv associate-/l/
1×frac-times frac-2neg div-sub associate-*r/ clear-num
Counts
4 → 135
Calls
4 calls:
32.0ms
(* (* 2.0 PI) u2)
76.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
45.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s
(/ (- (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series3.7s

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* 2.0 PI) u2)
1.0s
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
1.5s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s
(/ (- (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify681.0ms

Counts
147 → 147
Iterations

Useful iterations: done (673.0ms)

IterNodesCost
03474721
19764298
done50003831

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2)))
0.4b
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2)))
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b
(/ (- (* (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
474×add-exp-log
320×prod-exp
96×pow-exp
85×div-exp
54×add-cbrt-cube
48×pow-to-exp
31×add-sqr-sqrt
26×cbrt-unprod
22×add-cube-cbrt *-un-lft-identity
20×times-frac
15×associate-*r* associate-*l*
12×associate-*l/
10×cbrt-undiv
6×unswap-sqr sqr-pow
4×pow1 add-log-exp
3×unpow-prod-down associate-/r* *-commutative associate-/l*
2×frac-times flip3-- associate-*r/ associate-/r/ flip-- div-inv associate-/l/
1×frac-2neg div-sub clear-num
Counts
4 → 224
Calls
4 calls:
252.0ms
(* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2)))
68.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2)))
37.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
2.7s
(/ (- (* (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series4.1s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2)))
1.1s
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2)))
983.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0s
(/ (- (* (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (pow (* -2.0 (log u1)) (/ (* 2 0.5) 2))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify740.0ms

Counts
236 → 236
Iterations

Useful iterations: done (729.0ms)

IterNodesCost
03899274
111517094
done50015827

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes515.0ms

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

sample2.5s

Algorithm
intervals
Results
1.4s8000×body80valid
785.0ms8000×pre80true