Details

Time bar (total: 18.1s)

sample283.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
4.0ms256×pre80true

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
26819
314719
439519
5129319
done500019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

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)
0.2b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite48.0ms

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:
23.0ms
(+ (* (* (/ 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:
469.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
263.0ms
(pow (* -2.0 (log u1)) 0.5)
37.0ms
(* (* 2.0 PI) u2)
701.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify789.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (192.0ms)

IterNodesCost
02031408
15061344
217211222
done50001222

prune335.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize20.0ms

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

rewrite54.0ms

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)
6.0ms
(* (* 2.0 PI) u2)
16.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
25.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

series1.8s

Counts
4 → 12
Calls
4 calls:
267.0ms
(pow (* -2.0 (log u1)) 0.5)
40.0ms
(* (* 2.0 PI) u2)
707.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
749.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

simplify944.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (151.0ms)

IterNodesCost
02001773
14471551
214401422
done50011422

prune450.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) u2)
0.3b
(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
0.3b
(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
23×prod-exp
22×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
11×pow1 times-frac
9×rem-log-exp
8×div-exp associate-*r* pow-exp
5×cbrt-unprod
4×pow-to-exp exp-prod add-log-exp unswap-sqr
3×pow-prod-down associate-*l/ sqr-pow
2×log-div log-prod log-pow *-commutative
1×cbrt-undiv unpow-prod-down exp-diff exp-sum div-inv rem-exp-log
Counts
4 → 92
Calls
4 calls:
6.0ms
(* (* 2.0 PI) u2)
6.0ms
(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
12.0ms
(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
10.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* 2.0 PI) u2)
847.0ms
(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
705.0ms
(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
717.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.1s

Counts
104 → 104
Iterations

Useful iterations: 2 (285.0ms)

IterNodesCost
01761239
13951163
213191049
done50001049

prune359.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) u2)
0.4b
(* (/ 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))

rewrite331.0ms

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×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 → 135
Calls
4 calls:
6.0ms
(* (* 2.0 PI) u2)
10.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
21.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
289.0ms
(/ (- (* (* (* (/ 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))

series2.2s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 2.0 PI) u2)
699.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
705.0ms
(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
756.0ms
(/ (- (* (* (* (/ 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))

simplify1.2s

Counts
147 → 147
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03474721
19184292
236253801
done50003795

prune638.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes314.0ms

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

sample915.0ms

Algorithm
intervals
Results
637.0ms8000×body80valid
129.0ms8000×pre80true