Details

Time bar (total: 17.2s)

sample284.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
4.0ms256×pre80true

simplify834.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01819
13518
27118
315418
442918
5143618
done500018

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

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

rewrite44.0ms

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×expm1-log1p-u div-exp pow-prod-down log1p-expm1-u unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative fma-def flip3-+ associate-*l/ sum-log flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
19.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
2.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
13.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

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)
270.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* (* 2.0 PI) u2)
691.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify774.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (173.0ms)

IterNodesCost
02111496
15341416
221021295
done50001295

prune352.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×times-frac
12×pow1
11×add-cbrt-cube
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp log1p-expm1-u
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative fma-def frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv
Counts
4 → 93
Calls
4 calls:
18.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
2.0ms
(pow (* -2.0 (log u1)) 0.5)
7.0ms
(* (* 2.0 PI) u2)
4.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
447.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
258.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
703.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify673.0ms

Counts
105 → 105
Iterations

Useful iterations: 2 (159.0ms)

IterNodesCost
02031447
14651384
218061275
done50001275

prune349.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.9b
(expm1 (/ (pow (* -2.0 (log u1)) 0.5) 6.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×times-frac
12×pow1
11×add-cbrt-cube
5×unpow-prod-down prod-exp log1p-expm1-u associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp add-log-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv expm1-log1p frac-2neg associate-*l* clear-num *-commutative div-inv expm1-udef
Counts
4 → 90
Calls
4 calls:
2.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
4.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.0ms
(expm1 (/ (pow (* -2.0 (log u1)) 0.5) 6.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
262.0ms
(pow (* -2.0 (log u1)) 0.5)
37.0ms
(* (* 2.0 PI) u2)
694.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
755.0ms
(expm1 (/ (pow (* -2.0 (log u1)) 0.5) 6.0))

simplify2.9s

Counts
102 → 102
Iterations

Useful iterations: 3 (548.0ms)

IterNodesCost
01761143
13511093
211861011
349551002
done50001002

prune359.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite343.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 143
Calls
4 calls:
6.0ms
(* (* 2.0 PI) u2)
22.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
10.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
299.0ms
(/ (- (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* 2.0 PI) u2)
712.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
701.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
751.0ms
(/ (- (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify1.5s

Counts
155 → 155
Iterations

Useful iterations: 2 (365.0ms)

IterNodesCost
03554899
19564454
241723943
done50003943

prune608.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes318.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02021
12621
done2621

end0.0ms

sample910.0ms

Algorithm
intervals
Results
642.0ms8000×body80valid
119.0ms8000×pre80true