Details

Time bar (total: 25.0s)

sample128.0ms

Algorithm
intervals
Results
51.0ms256×body80valid
9.0ms256×pre80true

simplify3.7s

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: 0.4b

localize44.0ms

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)
0.2b
(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))

rewrite179.0ms

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:
80.0ms
(+ (* (* (/ 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)
24.0ms
(* (* 2.0 PI) u2)
61.0ms
(* (/ 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)
398.0ms
(pow (* -2.0 (log u1)) 0.5)
53.0ms
(* (* 2.0 PI) u2)
991.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02031408
14991344
216551222
done50001191

prune547.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
0.2b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
14×add-cbrt-cube
12×pow1
9×prod-exp
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×div-exp
4×pow-prod-down pow-exp cbrt-unprod
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×+-commutative unpow-prod-down frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv associate-/l* sqr-pow
Counts
4 → 70
Calls
4 calls:
55.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
13.0ms
(pow (* -2.0 (log u1)) 0.5)
30.0ms
(* (* 2.0 PI) u2)
15.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series2.4s

Counts
4 → 12
Calls
4 calls:
792.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
384.0ms
(pow (* -2.0 (log u1)) 0.5)
53.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01841168
14491121
21535986
done5000955

prune456.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
23×add-cbrt-cube
21×pow1
15×prod-exp
12×associate-*r*
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×pow-prod-down cbrt-unprod
6×sqrt-prod
5×div-exp
4×pow-exp add-log-exp
3×pow-unpow times-frac associate-/r*
2×cbrt-undiv pow-to-exp pow-pow associate-*l* *-commutative
1×unpow-prod-down frac-2neg clear-num div-inv associate-/l* sqr-pow
Counts
4 → 86
Calls
4 calls:
7.0ms
(pow (* -2.0 (log u1)) 0.5)
78.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
28.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
40.0ms
(* (* 2.0 PI) (sqrt u2))

series1.8s

Counts
4 → 12
Calls
4 calls:
440.0ms
(pow (* -2.0 (log u1)) 0.5)
71.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
1.2s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
112.0ms
(* (* 2.0 PI) (sqrt u2))

simplify2.1s

Counts
98 → 98
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01951164
1486989
21630848
done5001832

prune451.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(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))

rewrite207.0ms

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:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
117.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
18.0ms
(* (* 2.0 PI) u2)
50.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.7s

Counts
4 → 12
Calls
4 calls:
355.0ms
(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)))
61.0ms
(* (* 2.0 PI) u2)
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.7s

Counts
124 → 124
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02001773
14421551
214271422
done50011413

prune642.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes570.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02025
12725
done2725

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.5s8000×body80valid
393.0ms8000×pre80true