Details

Time bar (total: 30.3s)

sample223.0ms

Algorithm
intervals
Results
78.0ms256×body80valid
16.0ms256×pre80true

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5000
51672
4553
3171
274
136
018

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
0.2b
(* (* 2 PI) u2)
0.2b
(pow (* -2 (log u1)) 0.5)
0.4b
(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
25×add-sqr-sqrt
24×prod-exp
16×*-un-lft-identity
14×add-cbrt-cube associate-*l* add-cube-cbrt
13×times-frac
12×pow1
10×pow-exp
8×div-exp associate-*r*
6×add-log-exp unswap-sqr
5×pow-to-exp cbrt-unprod sqr-pow
4×rec-exp 1-exp pow-prod-down insert-posit16
3×pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative sum-log flip3-+ associate-*l/ flip-+ div-inv
Counts
4 → 101
Calls
4 calls:
54.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
35.0ms
(* (* 2 PI) u2)
7.0ms
(pow (* -2 (log u1)) 0.5)
18.0ms
(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
625.0ms
(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
65.0ms
(* (* 2 PI) u2)
420.0ms
(pow (* -2 (log u1)) 0.5)
1.0s
(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

simplify1.6s

Counts
113 → 113
Iterations
IterNodes
done5001
21943
1574
0218

prune660.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2 PI) u2)
0.2b
(pow (* -2 (log u1)) 0.5)
0.3b
(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
0.3b
(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
34×add-exp-log
33×associate-*l*
32×sqrt-prod
25×*-un-lft-identity
23×add-cube-cbrt
22×times-frac
19×prod-exp
16×add-cbrt-cube
14×pow1
9×associate-*r*
8×unswap-sqr
7×cbrt-unprod
6×pow-exp sqr-pow
5×sqrt-div pow-prod-down
4×associate-*l/ insert-posit16 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 → 118
Calls
4 calls:
16.0ms
(* (* 2 PI) u2)
9.0ms
(pow (* -2 (log u1)) 0.5)
63.0ms
(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
18.0ms
(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

series2.7s

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* 2 PI) u2)
671.0ms
(pow (* -2 (log u1)) 0.5)
1.1s
(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
952.0ms
(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

simplify1.5s

Counts
130 → 130
Iterations
IterNodes
done5000
21436
1489
0201

prune937.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (* 2 PI) u2)) (cbrt (* (* 2 PI) u2)))
0.6b
(cbrt (* (* 2 PI) u2))
0.6b
(cbrt (* (* 2 PI) u2))
0.6b
(cbrt (* (* 2 PI) u2))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 62
Calls
4 calls:
55.0ms
(* (cbrt (* (* 2 PI) u2)) (cbrt (* (* 2 PI) u2)))
20.0ms
(cbrt (* (* 2 PI) u2))
20.0ms
(cbrt (* (* 2 PI) u2))
20.0ms
(cbrt (* (* 2 PI) u2))

series1.6s

Counts
4 → 12
Calls
4 calls:
504.0ms
(* (cbrt (* (* 2 PI) u2)) (cbrt (* (* 2 PI) u2)))
308.0ms
(cbrt (* (* 2 PI) u2))
369.0ms
(cbrt (* (* 2 PI) u2))
410.0ms
(cbrt (* (* 2 PI) u2))

simplify2.8s

Counts
74 → 74
Iterations
IterNodes
done5000
43921
31393
2577
1203
085

prune726.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/36 (* (* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))) (pow (* (log u1) -2) 0.5)))
0.4b
(* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)))
0.5b
(cbrt (* 1/36 (* (* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))) (pow (* (log u1) -2) 0.5))))
0.6b
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
436×add-exp-log
392×prod-exp
132×pow-exp
66×pow-to-exp
25×add-cbrt-cube
15×add-sqr-sqrt
14×cbrt-unprod
11×associate-*l*
10×*-un-lft-identity add-cube-cbrt
8×pow1 sqr-pow
7×associate-*r*
5×swap-sqr unswap-sqr
4×unpow-prod-down insert-posit16 add-log-exp
3×pow-prod-down *-commutative
1×cbrt-prod pow2 pow1/3 pow-sqr pow-prod-up
Counts
4 → 184
Calls
4 calls:
276.0ms
(* 1/36 (* (* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))) (pow (* (log u1) -2) 0.5)))
55.0ms
(* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)))
170.0ms
(cbrt (* 1/36 (* (* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))) (pow (* (log u1) -2) 0.5))))
28.0ms
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))

series4.0s

Counts
4 → 12
Calls
4 calls:
999.0ms
(* 1/36 (* (* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))) (pow (* (log u1) -2) 0.5)))
948.0ms
(* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)))
1.1s
(cbrt (* 1/36 (* (* 1/6 (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))) (pow (* (log u1) -2) 0.5))))
984.0ms
(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))

simplify2.7s

Counts
196 → 196
Iterations
IterNodes
done5002
22019
1679
0262

prune784.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes548.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done35
335
233
131
021

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.4s8000×body80valid
374.0ms8000×pre80true