Details

Time bar (total: 18.3s)

sample346.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
4.0ms256×pre80true

simplify2.5s

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: 0.3b

localize26.0ms

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

rewrite115.0ms

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)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
18.0ms
(* (* 2.0 PI) u2)
25.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts
4 → 12
Calls
4 calls:
457.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
254.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* (* 2.0 PI) u2)
695.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify900.0ms

Counts
99 → 99
Iterations

Useful iterations: done (896.0ms)

IterNodesCost
02031408
14991344
216551222
done50001191

prune313.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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

rewrite116.0ms

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)
62.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
17.0ms
(* (* 2.0 PI) u2)
26.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.7s

Counts
4 → 12
Calls
4 calls:
269.0ms
(pow (* -2.0 (log u1)) 0.5)
721.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
32.0ms
(* (* 2.0 PI) u2)
700.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.2s

Counts
124 → 124
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02001773
14421551
214271422
done50011413

prune426.0ms

Pruning

5 alts after pruning (5 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)) (* 1 (pow (* -2.0 (log u1)) 0.5))))
0.2b
(* (* 2.0 PI) u2)
0.3b
(* (sqrt (/ 1.0 6.0)) (* 1 (pow (* -2.0 (log u1)) 0.5)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
52×prod-exp
33×associate-*l*
26×sqrt-prod
23×add-cbrt-cube
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
19×pow1
18×times-frac
12×cbrt-unprod
10×pow-exp
8×1-exp pow-prod-down
5×pow-to-exp sqrt-div associate-*r*
4×associate-*l/ add-log-exp
3×pow-unpow *-commutative
2×pow-pow div-inv
1×frac-times unpow-prod-down associate-*r/ sqr-pow
Counts
4 → 116
Calls
4 calls:
6.0ms
(pow (* -2.0 (log u1)) 0.5)
106.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (* 1 (pow (* -2.0 (log u1)) 0.5))))
17.0ms
(* (* 2.0 PI) u2)
40.0ms
(* (sqrt (/ 1.0 6.0)) (* 1 (pow (* -2.0 (log u1)) 0.5)))

series1.7s

Counts
4 → 12
Calls
4 calls:
257.0ms
(pow (* -2.0 (log u1)) 0.5)
737.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (* 1 (pow (* -2.0 (log u1)) 0.5))))
32.0ms
(* (* 2.0 PI) u2)
697.0ms
(* (sqrt (/ 1.0 6.0)) (* 1 (pow (* -2.0 (log u1)) 0.5)))

simplify1.5s

Counts
128 → 128
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02172022
14941525
214771364
done50001355

prune383.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b
(pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5)
0.2b
(* (* 2.0 PI) u2)
0.3b
(* (pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5) 0.16666666666666666)

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
163×add-exp-log
150×prod-exp
118×pow-exp
58×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
5×pow-prod-down
4×cbrt-unprod
3×pow-unpow sqr-pow
2×unpow-prod-down pow-pow *-commutative unswap-sqr
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 127
Calls
4 calls:
63.0ms
(+ (* (* (pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2))) 0.5)
39.0ms
(pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5)
17.0ms
(* (* 2.0 PI) u2)
40.0ms
(* (pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5) 0.16666666666666666)

series2.8s

Counts
4 → 12
Calls
4 calls:
471.0ms
(+ (* (* (pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2))) 0.5)
1.1s
(pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5)
38.0ms
(* (* 2.0 PI) u2)
1.1s
(* (pow (* (* (pow (- (log u1)) 1.0) (pow -2.0 1.0)) (pow -1 1.0)) 0.5) 0.16666666666666666)

simplify960.0ms

Counts
139 → 139
Iterations

Useful iterations: done (955.0ms)

IterNodesCost
02472865
16052631
218162393
done50002364

prune309.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes247.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02227
13225
done3225

end0.0ms

sample956.0ms

Algorithm
intervals
Results
641.0ms8000×body80valid
115.0ms8000×pre80true