Details

Time bar (total: 17.1s)

sample291.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
5.0ms256×pre80true

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
01819
13518
27118
315318
442318
5139418
done500018

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (/ 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))

rewrite32.0ms

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
5×cbrt-unprod
4×expm1-log1p-u div-exp pow-prod-down log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv associate-*l/ fma-udef div-inv
Counts
4 → 92
Calls
4 calls:
0.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
3.0ms
(pow (* -2.0 (log u1)) 0.5)
7.0ms
(* (* 2.0 PI) u2)
13.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts
4 → 12
Calls
4 calls:
478.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
272.0ms
(pow (* -2.0 (log u1)) 0.5)
39.0ms
(* (* 2.0 PI) u2)
727.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify916.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (176.0ms)

IterNodesCost
01971340
14541286
215261166
done50001166

prune376.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (* 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)

rewrite16.0ms

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
5×div-exp
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×unpow-prod-down frac-2neg associate-*l* clear-num *-commutative fma-udef div-inv associate-/l* sqr-pow
Counts
4 → 75
Calls
4 calls:
0.0ms
(fma (/ (* 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)

series1.5s

Counts
4 → 12
Calls
4 calls:
475.0ms
(fma (/ (* 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)
33.0ms
(* (* 2.0 PI) u2)
731.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify798.0ms

Counts
87 → 87
Iterations

Useful iterations: 2 (136.0ms)

IterNodesCost
01781100
14031053
21378930
done5000930

prune320.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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×expm1-log1p-u associate-*l/ log1p-expm1-u 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 → 120
Calls
4 calls:
3.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
26.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
13.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.8s

Counts
4 → 12
Calls
4 calls:
271.0ms
(pow (* -2.0 (log u1)) 0.5)
39.0ms
(* (* 2.0 PI) u2)
772.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
740.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.1s

Counts
132 → 132
Iterations

Useful iterations: 2 (159.0ms)

IterNodesCost
02081857
14551623
214581494
done50001494

prune524.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize19.0ms

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)))

rewrite27.0ms

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×expm1-log1p-u pow-prod-down log1p-expm1-u 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 → 132
Calls
4 calls:
2.0ms
(pow (* -2.0 (log u1)) 0.5)
7.0ms
(* (* 2.0 PI) u2)
9.0ms
(/ 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)))

series1.9s

Counts
4 → 12
Calls
4 calls:
270.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* (* 2.0 PI) u2)
722.0ms
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
917.0ms
(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

simplify1.1s

Counts
144 → 144
Iterations

Useful iterations: 2 (243.0ms)

IterNodesCost
02381984
15381804
216461568
done50011568

prune356.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes352.0ms

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
01718
12118
done2118

end0.0ms

sample921.0ms

Algorithm
intervals
Results
646.0ms8000×body80valid
129.0ms8000×pre80true