Details

Time bar (total: 14.6s)

sample282.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
4.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
26819
314719
439519
5129119
done500019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

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)
0.2b
(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))

rewrite48.0ms

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:
23.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
3.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
12.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts
4 → 12
Calls
4 calls:
450.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
259.0ms
(pow (* -2.0 (log u1)) 0.5)
37.0ms
(* (* 2.0 PI) u2)
693.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify642.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
02031408
15061344
217211222
done50001222

prune326.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

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

rewrite27.0ms

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:
11.0ms
(+ (* (/ (* 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)
5.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
6.0ms
(* (* 2.0 PI) u2)

series1.4s

Counts
4 → 12
Calls
4 calls:
450.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
260.0ms
(pow (* -2.0 (log u1)) 0.5)
685.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
32.0ms
(* (* 2.0 PI) u2)

simplify558.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (150.0ms)

IterNodesCost
01841168
14551121
21563986
done5001986

prune259.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b
(/ (* 1.0 (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))) 6.0)
0.3b
(* (* 2.0 PI) u2)
0.5b
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
113×add-exp-log
69×prod-exp
34×pow-exp
22×add-sqr-sqrt
20×add-cbrt-cube
18×add-cube-cbrt *-un-lft-identity div-exp
17×pow-to-exp
13×pow-unpow
12×pow1 times-frac
9×sqr-pow
8×associate-*r*
7×cbrt-unprod
6×associate-*l*
5×unpow-prod-down swap-sqr pow-prod-down
4×add-log-exp unswap-sqr
3×cbrt-undiv associate-/r*
2×pow-pow *-commutative div-inv
1×pow2 frac-2neg clear-num pow-sqr pow-prod-up associate-/l*
Counts
4 → 131
Calls
4 calls:
3.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
12.0ms
(/ (* 1.0 (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))) 6.0)
6.0ms
(* (* 2.0 PI) u2)
7.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
261.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
695.0ms
(/ (* 1.0 (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))) 6.0)
31.0ms
(* (* 2.0 PI) u2)
657.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify678.0ms

Counts
143 → 143
Iterations

Useful iterations: 2 (251.0ms)

IterNodesCost
02472762
16231667
220101479
done50011479

prune386.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 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))
0.5b
(/ (- (* (* (* (/ 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))

rewrite339.0ms

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×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:
6.0ms
(* (* 2.0 PI) u2)
21.0ms
(* (* (/ 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))
297.0ms
(/ (- (* (* (* (/ 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))

series2.3s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 2.0 PI) u2)
668.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
799.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
761.0ms
(/ (- (* (* (* (/ 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))

simplify1.3s

Counts
147 → 147
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03474721
19184292
236403801
done50003795

prune603.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes334.0ms

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
01819
12419
done2419

end0.0ms

sample885.0ms

Algorithm
intervals
Results
618.0ms8000×body80valid
125.0ms8000×pre80true