Details

Time bar (total: 11.1s)

sample324.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
4.0ms256×pre80true

simplify91.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03410
17110
215410
346910
4181210
5500110
done500110

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (/ 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))

rewrite115.0ms

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:
56.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
11.0ms
(pow (* -2.0 (log u1)) 0.5)
17.0ms
(* (* 2.0 PI) u2)
25.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts
4 → 12
Calls
4 calls:
473.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
267.0ms
(pow (* -2.0 (log u1)) 0.5)
40.0ms
(* (* 2.0 PI) u2)
695.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify59.0ms

Counts
99 → 99
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0507728
12155656
25001656
done5001656

prune319.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×times-frac
12×pow1
11×add-cbrt-cube
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×div-exp pow-prod-down pow-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv
Counts
4 → 84
Calls
4 calls:
49.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
20.0ms
(* (* 2.0 PI) u2)
9.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
473.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
268.0ms
(pow (* -2.0 (log u1)) 0.5)
39.0ms
(* (* 2.0 PI) u2)
690.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify51.0ms

Counts
96 → 96
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0438710
11838655
25001655
done5001655

prune311.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
24×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
14×associate-*l* add-cbrt-cube
13×prod-exp
11×pow1 times-frac
8×associate-*r*
6×log-prod
5×cbrt-unprod
4×log-div exp-prod div-exp pow-exp add-log-exp unswap-sqr
3×exp-sum pow-prod-down sqr-pow
2×pow-to-exp flip3-+ exp-diff log-pow *-commutative flip-+
1×cbrt-undiv unpow-prod-down rem-log-exp associate-*l/ div-inv rem-exp-log
Counts
4 → 90
Calls
4 calls:
84.0ms
(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
17.0ms
(* (* 2.0 PI) u2)
85.0ms
(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
26.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.7s

Counts
4 → 12
Calls
4 calls:
542.0ms
(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
33.0ms
(* (* 2.0 PI) u2)
461.0ms
(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
693.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify56.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05111079
11983972
25001954
done5001954

prune372.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite325.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
33×associate-*l*
31×add-exp-log
30×sqrt-prod
24×add-cube-cbrt *-un-lft-identity
20×times-frac
18×prod-exp
16×add-cbrt-cube
12×pow1
9×associate-*r*
7×cbrt-unprod
6×unswap-sqr
5×sqrt-div
4×exp-prod pow-prod-down associate-*l/ pow-exp add-log-exp sqr-pow
3×log-prod exp-sum *-commutative
2×pow-to-exp log-div exp-diff div-inv
1×frac-times unpow-prod-down flip3-+ associate-*r/ log-pow flip-+ rem-exp-log
Counts
4 → 112
Calls
4 calls:
59.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
17.0ms
(* (* 2.0 PI) u2)
219.0ms
(exp (log (+ (* (* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))) (cos (* (* 2.0 PI) u2))) 0.5)))
26.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.0s

Counts
4 → 12
Calls
4 calls:
751.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
33.0ms
(* (* 2.0 PI) u2)
527.0ms
(exp (log (+ (* (* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))) (cos (* (* 2.0 PI) u2))) 0.5)))
728.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify64.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05511283
122101141
250021103
done50021103

prune517.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes403.0ms

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
02410
12410
done2410

end0.0ms

sample977.0ms

Algorithm
intervals
Results
658.0ms8000×body80valid
115.0ms8000×pre80true