Details

Time bar (total: 15.4s)

sample280.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
5.0ms256×pre80true

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
26819
314719
439519
5129319
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)
0.1b
(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))

rewrite49.0ms

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:
24.0ms
(+ (* (* (/ 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)
12.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts
4 → 12
Calls
4 calls:
478.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
277.0ms
(pow (* -2.0 (log u1)) 0.5)
39.0ms
(* (* 2.0 PI) u2)
723.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify773.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (188.0ms)

IterNodesCost
02031408
15061344
217211222
done50001222

prune337.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize18.0ms

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

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)
3.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
5.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
478.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
273.0ms
(pow (* -2.0 (log u1)) 0.5)
34.0ms
(* (* 2.0 PI) u2)
722.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify681.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (151.0ms)

IterNodesCost
01841168
14551121
21566986
done5000986

prune264.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

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

rewrite55.0ms

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:
2.0ms
(pow (* -2.0 (log u1)) 0.5)
9.0ms
(* (* 2.0 PI) u2)
25.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
13.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.8s

Counts
4 → 12
Calls
4 calls:
269.0ms
(pow (* -2.0 (log u1)) 0.5)
40.0ms
(* (* 2.0 PI) u2)
764.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
727.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify935.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (149.0ms)

IterNodesCost
02001773
14471551
214421422
done50001422

prune576.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (* 1 (* (/ 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))

rewrite67.0ms

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:
45.0ms
(+ (* (* 1 (* (/ 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)
10.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts
4 → 12
Calls
4 calls:
468.0ms
(+ (* (* 1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))) (cos (* (* 2.0 PI) u2))) 0.5)
272.0ms
(pow (* -2.0 (log u1)) 0.5)
38.0ms
(* (* 2.0 PI) u2)
712.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify837.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (197.0ms)

IterNodesCost
02041444
15101344
217371222
done50001222

prune283.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes393.0ms

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
02025
12725
done2725

end0.0ms

sample925.0ms

Algorithm
intervals
Results
638.0ms8000×body80valid
131.0ms8000×pre80true