Details

Time bar (total: 16.9s)

sample292.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
5.0ms256×pre80true

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
26819
314719
441519
5137519
done500019

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)
0.2b
(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))

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×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:
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:
460.0ms
(+ (* (* (/ 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)
705.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify895.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (202.0ms)

IterNodesCost
02031408
15061344
217211222
done50001222

prune345.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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

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×pow-prod-down pow-exp cbrt-unprod
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×+-commutative unpow-prod-down frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv associate-/l* sqr-pow
Counts
4 → 70
Calls
4 calls:
11.0ms
(+ (* (/ (* 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)
6.0ms
(* (* 2.0 PI) u2)
5.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
444.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
258.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
705.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify767.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (167.0ms)

IterNodesCost
01841168
14551121
21566986
done5000986

prune259.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (* 2.0 PI) u2)
0.3b
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
0.3b
(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
36×times-frac
32×div-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity prod-exp
23×add-cbrt-cube
13×pow1
10×pow-exp
8×associate-/r*
7×cbrt-undiv
6×rec-exp 1-exp div-inv associate-/l*
5×pow-to-exp cbrt-unprod
4×pow-prod-down add-log-exp
3×pow-unpow associate-*r*
2×pow-pow frac-2neg clear-num
1×unpow-prod-down pow-flip associate-*l* associate-/r/ *-commutative inv-pow sqr-pow
Counts
4 → 124
Calls
4 calls:
2.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
8.0ms
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
4.0ms
(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

series1.8s

Counts
4 → 12
Calls
4 calls:
268.0ms
(pow (* -2.0 (log u1)) 0.5)
38.0ms
(* (* 2.0 PI) u2)
700.0ms
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
755.0ms
(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

simplify1.1s

Counts
136 → 136
Iterations

Useful iterations: 2 (257.0ms)

IterNodesCost
02301910
15301730
216341478
done50001478

prune449.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ 0.5 (* (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5) (cos (* (* 2.0 PI) u2))) 0.16666666666666666))
0.2b
(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5)
0.2b
(* (* 2.0 PI) u2)
0.3b
(* (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5) (cos (* (* 2.0 PI) u2))) 0.16666666666666666)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
198×add-exp-log
184×prod-exp
118×pow-exp
58×pow-to-exp
14×add-cbrt-cube
12×pow1
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down cbrt-unprod add-log-exp
3×pow-unpow
2×pow-pow associate-*l* *-commutative
1×+-commutative unpow-prod-down flip3-+ sum-log flip-+ sqr-pow
Counts
4 → 124
Calls
4 calls:
3.0ms
(+ 0.5 (* (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5) (cos (* (* 2.0 PI) u2))) 0.16666666666666666))
17.0ms
(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5)
6.0ms
(* (* 2.0 PI) u2)
30.0ms
(* (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5) (cos (* (* 2.0 PI) u2))) 0.16666666666666666)

series2.3s

Counts
4 → 12
Calls
4 calls:
457.0ms
(+ 0.5 (* (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5) (cos (* (* 2.0 PI) u2))) 0.16666666666666666))
1.1s
(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5)
36.0ms
(* (* 2.0 PI) u2)
651.0ms
(* (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5) (cos (* (* 2.0 PI) u2))) 0.16666666666666666)

simplify975.0ms

Counts
136 → 136
Iterations

Useful iterations: 2 (241.0ms)

IterNodesCost
02623245
16742920
220022631
done50012631

prune286.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes263.0ms

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

sample919.0ms

Algorithm
intervals
Results
636.0ms8000×body80valid
132.0ms8000×pre80true