Details

Time bar (total: 36.9s)

sample307.0ms

Algorithm
intervals
Results
31.0ms256×body80valid
6.0ms256×pre80true

simplify4.3s

Counts
1 → 1
Iterations
IterNodes
done5000
51534
4385
3145
269
134
018

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

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))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×*-un-lft-identity add-cbrt-cube associate-*l* prod-exp add-cube-cbrt
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 sum-log flip3-+ associate-*l/ 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)
10.0ms
(pow (* -2.0 (log u1)) 0.5)
26.0ms
(* (* 2.0 PI) u2)
38.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
684.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
394.0ms
(pow (* -2.0 (log u1)) 0.5)
37.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.2s

Counts
99 → 99
Iterations
IterNodes
done5001
21834
1555
0206

prune813.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt add-exp-log
33×associate-*l*
30×sqrt-prod
23×*-un-lft-identity add-cube-cbrt
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:
9.0ms
(pow (* -2.0 (log u1)) 0.5)
92.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
21.0ms
(* (* 2.0 PI) u2)
26.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts
4 → 12
Calls
4 calls:
438.0ms
(pow (* -2.0 (log u1)) 0.5)
949.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
41.0ms
(* (* 2.0 PI) u2)
908.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.9s

Counts
124 → 124
Iterations
IterNodes
done5000
21444
1485
0200

prune945.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
35×associate-*l*
31×add-exp-log
30×sqrt-prod
24×*-un-lft-identity add-cube-cbrt
20×times-frac
17×prod-exp
13×add-cbrt-cube
11×pow1
9×associate-*r*
7×unswap-sqr
6×pow-exp
5×sqrt-div cbrt-unprod sqr-pow
4×associate-*l/ add-log-exp
3×pow-to-exp pow-unpow pow-prod-down *-commutative
2×unpow-prod-down pow-pow div-inv
1×frac-times associate-*r/
Counts
4 → 112
Calls
4 calls:
9.0ms
(pow (* -2.0 (log u1)) 0.5)
85.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
6.0ms
(* u2 PI)
38.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.7s

Counts
4 → 12
Calls
4 calls:
399.0ms
(pow (* -2.0 (log u1)) 0.5)
1.1s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
37.0ms
(* u2 PI)
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify3.5s

Counts
124 → 124
Iterations
IterNodes
done5001
34029
21233
1447
0191

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize64.0ms

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
666×add-exp-log
500×prod-exp
96×add-cbrt-cube
89×div-exp
88×pow-exp
60×cbrt-unprod
45×add-sqr-sqrt
44×pow-to-exp
43×pow1
34×times-frac
29×*-un-lft-identity add-cube-cbrt
27×associate-*l*
17×pow-prod-down
11×cbrt-undiv associate-*r* associate-*l/
8×unswap-sqr
6×sqr-pow
4×pow-sqr pow-prod-up associate-/l* add-log-exp difference-of-squares
3×associate-/r* *-commutative div-inv
2×unpow-prod-down pow-plus flip3-- associate-/r/ flip-- associate-/l/
1×pow2 frac-times clear-num frac-2neg div-sub swap-sqr associate-*r/
Counts
4 → 263
Calls
4 calls:
18.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
23.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0s
(/ (- (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
411.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

series4.0s

Counts
4 → 12
Calls
4 calls:
968.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.2s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s
(/ (- (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
766.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

simplify3.3s

Counts
275 → 275
Iterations
IterNodes
done5001
23269
1977
0368

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes1.2s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done29
129
020

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.4s8000×body80valid
253.0ms8000×pre80true