Details

Time bar (total: 15.0s)

sample290.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
5.0ms256×pre80true

simplify809.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
01819
13518
27118
315418
442918
5143418
done500118

prune10.0ms

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))

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×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:
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:
466.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
275.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* (* 2.0 PI) u2)
707.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify672.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
02111496
15341416
219511295
done50011295

prune360.0ms

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×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod log1p-expm1-u
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×+-commutative unpow-prod-down fma-def frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv associate-/l* sqr-pow
Counts
4 → 79
Calls
4 calls:
12.0ms
(+ (* (/ (* 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)
7.0ms
(* (* 2.0 PI) u2)

series1.5s

Counts
4 → 12
Calls
4 calls:
470.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
271.0ms
(pow (* -2.0 (log u1)) 0.5)
716.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
33.0ms
(* (* 2.0 PI) u2)

simplify595.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (154.0ms)

IterNodesCost
01921256
14881191
217581059
done50001059

prune300.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize20.0ms

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)))

rewrite40.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 139
Calls
4 calls:
4.0ms
(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)
8.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
263.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
723.0ms
(/ (* 1.0 (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))) 6.0)
32.0ms
(* (* 2.0 PI) u2)
685.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify748.0ms

Counts
151 → 151
Iterations

Useful iterations: 2 (208.0ms)

IterNodesCost
02552872
16561733
222351545
done50001545

prune405.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize28.0ms

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 PI) u2)) (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))

rewrite344.0ms

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×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:
6.0ms
(* (* 2.0 PI) u2)
22.0ms
(* (* (/ 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))
300.0ms
(/ (- (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* (* 2.0 PI) u2)) (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))

series2.4s

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* 2.0 PI) u2)
684.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
866.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
795.0ms
(/ (- (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* (* 2.0 PI) u2)) (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))

simplify1.3s

Counts
155 → 155
Iterations

Useful iterations: 2 (334.0ms)

IterNodesCost
03554899
19564454
240693943
done50003943

prune633.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes315.0ms

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

sample954.0ms

Algorithm
intervals
Results
680.0ms8000×body80valid
119.0ms8000×pre80true