Details

Time bar (total: 29.6s)

sample265.0ms

Algorithm
intervals
Results
56.0ms256×body80valid
11.0ms256×pre80true

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01819
13419
27119
315219
444019
5138519
done500019

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (/ 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)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite186.0ms

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:
86.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* (* 2.0 PI) u2)
57.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
625.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
403.0ms
(pow (* -2.0 (log u1)) 0.5)
73.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.9s

Counts
99 → 99
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02031408
14991344
216551222
done50001191

prune491.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 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))

rewrite150.0ms

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:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
35.0ms
(* (* 2.0 PI) u2)
72.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
26.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.6s

Counts
4 → 12
Calls
4 calls:
502.0ms
(pow (* -2.0 (log u1)) 0.5)
48.0ms
(* (* 2.0 PI) u2)
1.0s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
1.0s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.8s

Counts
124 → 124
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02001773
14421551
214201428
done50001413

prune743.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (/ 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)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite175.0ms

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)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
18.0ms
(* (* 2.0 PI) u2)
54.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.4s

Counts
4 → 12
Calls
4 calls:
669.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
508.0ms
(pow (* -2.0 (log u1)) 0.5)
75.0ms
(* (* 2.0 PI) u2)
1.2s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02031408
14991344
216551222
done50001191

prune429.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (- 0.5 (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))))
0.8b
(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

rewrite417.0ms

Algorithm
rewrite-expression-head
Rules
116×add-exp-log
68×prod-exp
38×add-sqr-sqrt add-cbrt-cube
27×associate-*l*
26×pow-exp
22×add-cube-cbrt *-un-lft-identity times-frac
18×cbrt-unprod
16×div-exp
13×associate-*r*
12×pow1
11×associate-*l/
9×pow-to-exp
8×unswap-sqr
7×sqr-pow
4×cbrt-undiv pow-prod-down add-log-exp rem-cube-cbrt
3×unpow-prod-down pow-unpow *-commutative
2×distribute-rgt-in frac-times sub-neg flip3-- pow-pow distribute-lft-in associate-*r/ flip-- div-inv
1×cube-div cube-mult unpow3 cube-prod
Counts
4 → 152
Calls
4 calls:
43.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
22.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
246.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (- 0.5 (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))))
91.0ms
(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

series4.4s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.4s
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (- 0.5 (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))))
830.0ms
(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

simplify1.9s

Counts
164 → 164
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02724188
16913818
227503361
done50003346

prune907.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes546.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01819
12419
done2419

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.6s8000×body80valid
777.0ms8000×pre80true