Details

Time bar (total: 34.3s)

sample125.0ms

Algorithm
intervals
Results
39.0ms256×body80valid
8.0ms256×pre80true

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
01819
13518
27218
315618
445018
5140718
done500018

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

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

rewrite185.0ms

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:
98.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
13.0ms
(pow (* -2.0 (log u1)) 0.5)
27.0ms
(* (* 2.0 PI) u2)
42.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
663.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
383.0ms
(pow (* -2.0 (log u1)) 0.5)
54.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.4s

Counts
108 → 108
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02111496
15151416
216951295
done50011265

prune541.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

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×expm1-log1p-u associate-*l/ log1p-expm1-u 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 → 120
Calls
4 calls:
14.0ms
(pow (* -2.0 (log u1)) 0.5)
93.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
51.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
29.0ms
(* (* 2.0 PI) u2)

series3.0s

Counts
4 → 12
Calls
4 calls:
404.0ms
(pow (* -2.0 (log u1)) 0.5)
1.2s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
1.3s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
63.0ms
(* (* 2.0 PI) u2)

simplify1.9s

Counts
132 → 132
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02081857
14501623
214361494
done50001485

prune751.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 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))

rewrite1.7s

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:
19.0ms
(* (* 2.0 PI) u2)
31.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
105.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
1.5s
(/ (- (* (* (* (/ 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))

series3.3s

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0s
(* (* (/ 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))

simplify2.3s

Counts
155 → 155
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03554899
19084454
235423949
done50013933

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b
(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×add-sqr-sqrt
14×associate-*l* add-cbrt-cube
13×add-cube-cbrt *-un-lft-identity prod-exp
11×times-frac
9×pow1
8×associate-*r*
5×expm1-log1p-u cbrt-unprod
4×div-exp pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down sqr-pow
2×pow-to-exp *-commutative
1×cbrt-undiv unpow-prod-down log1p-udef expm1-log1p log1p-expm1 associate-*l/ div-inv expm1-udef
Counts
4 → 85
Calls
4 calls:
0.0ms
(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
18.0ms
(* (* 2.0 PI) u2)
45.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0ms
(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

series4.1s

Counts
4 → 12
Calls
4 calls:
1.3s
(log1p (* (/ 1.0 6.0) (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))
1.5s
(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

simplify3.6s

Counts
97 → 97
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01801251
13851178
212131060
343841051
done50001051

prune551.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes593.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01921
12521
done2521

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.9s8000×body80valid
345.0ms8000×pre80true