Details

Time bar (total: 29.3s)

sample250.0ms

Algorithm
intervals
Results
54.0ms256×body80valid
10.0ms256×pre80true

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
01819
13419
27119
315519
447219
5316119
done500019

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize60.0ms

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))

rewrite209.0ms

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:
90.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
24.0ms
(pow (* -2.0 (log u1)) 0.5)
36.0ms
(* (* 2.0 PI) u2)
51.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
725.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
387.0ms
(pow (* -2.0 (log u1)) 0.5)
45.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
99 → 99
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02031408
15471350
225481230
done50001207

prune667.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize51.0ms

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

rewrite130.0ms

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×div-exp pow-prod-down pow-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv
Counts
4 → 84
Calls
4 calls:
73.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
9.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
37.0ms
(* (* 2.0 PI) u2)

series2.2s

Counts
4 → 12
Calls
4 calls:
639.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
439.0ms
(pow (* -2.0 (log u1)) 0.5)
1.0s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
52.0ms
(* (* 2.0 PI) u2)

simplify1.4s

Counts
96 → 96
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01951363
14821321
221591224
done50011181

prune648.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) u2)
0.3b
(* (/ 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)))
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))

rewrite1.3s

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:
21.0ms
(* (* 2.0 PI) u2)
44.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
84.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
1.1s
(/ (- (* (* (* (/ 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))

series3.6s

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* 2.0 PI) u2)
995.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.4s
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
1.1s
(/ (- (* (* (* (/ 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))

simplify687.0ms

Counts
147 → 147
Iterations

Useful iterations: done (679.0ms)

IterNodesCost
03474721
19794298
done50003841

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
0.3b
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
76×add-exp-log
43×add-sqr-sqrt times-frac
34×prod-exp
32×add-cube-cbrt *-un-lft-identity
22×associate-*r* pow-exp
20×div-exp
16×add-cbrt-cube
14×sqr-pow
13×pow-unpow
12×pow1
11×pow-to-exp
9×unpow-prod-down
6×associate-*l* unswap-sqr
5×cbrt-unprod associate-/l*
4×pow-prod-down add-log-exp
3×associate-/r* div-inv
2×cbrt-undiv pow-pow *-commutative
1×frac-2neg associate-*r/ clear-num
Counts
4 → 144
Calls
4 calls:
8.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
18.0ms
(* (* 2.0 PI) u2)
9.0ms
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
54.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0))

series2.8s

Counts
4 → 12
Calls
4 calls:
462.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
66.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
1.2s
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0))

simplify2.7s

Counts
156 → 156
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02382775
16222614
235622027
done50011967

prune1.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes1.0s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01819
12419
done2419

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.1s8000×body80valid
242.0ms8000×pre80true