Details

Time bar (total: 27.0s)

sample319.0ms

Algorithm
intervals
Results
56.0ms256×body80valid
11.0ms256×pre80true

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
01819
13419
27119
315219
444019
5138519
done500019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

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))

rewrite178.0ms

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:
88.0ms
(+ (* (* (/ 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)
36.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts
4 → 12
Calls
4 calls:
719.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
439.0ms
(pow (* -2.0 (log u1)) 0.5)
48.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.3s

Counts
99 → 99
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02031408
14991344
216551222
done50001191

prune485.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize24.0ms

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)

rewrite197.0ms

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:
7.0ms
(pow (* -2.0 (log u1)) 0.5)
120.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
29.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
36.0ms
(* (* 2.0 PI) u2)

series2.8s

Counts
4 → 12
Calls
4 calls:
437.0ms
(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)))
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
60.0ms
(* (* 2.0 PI) u2)

simplify1.8s

Counts
124 → 124
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02001773
14421551
214191422
done50001413

prune666.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (* 1 (* (/ 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))

rewrite251.0ms

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:
176.0ms
(+ (* (* 1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))) (cos (* (* 2.0 PI) u2))) 0.5)
12.0ms
(pow (* -2.0 (log u1)) 0.5)
34.0ms
(* (* 2.0 PI) u2)
24.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.6s

Counts
4 → 12
Calls
4 calls:
656.0ms
(+ (* (* 1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))) (cos (* (* 2.0 PI) u2))) 0.5)
441.0ms
(pow (* -2.0 (log u1)) 0.5)
67.0ms
(* (* 2.0 PI) u2)
1.4s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.5s

Counts
99 → 99
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02041444
15021344
216731222
done50001191

prune561.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize61.0ms

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))
0.5b
(/ (- (* (* (* (/ 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))

rewrite1.4s

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:
35.0ms
(* (* 2.0 PI) u2)
81.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
35.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.2s
(/ (- (* (* (* (/ 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))

series3.3s

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* 2.0 PI) u2)
1.1s
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.2s
(/ (- (* (* (* (/ 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))

simplify2.1s

Counts
147 → 147
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03474721
18854292
234603801
done50013793

prune956.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes7.0ms