Details

Time bar (total: 26.1s)

sample129.0ms

Algorithm
intervals
Results
37.0ms256×body80valid
7.0ms256×pre80true

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
01819
13518
27218
315918
448318
5314018
done500118

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:

0.0b
(fma (* (/ 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))

rewrite71.0ms

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)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
25.0ms
(* (* 2.0 PI) u2)
32.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
732.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
373.0ms
(pow (* -2.0 (log u1)) 0.5)
63.0ms
(* (* 2.0 PI) u2)
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
104 → 104
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01971340
14941292
223001170
done50001151

prune524.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* (/ 1 1) (/ (* 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)
0.2b
(* (* 2.0 PI) u2)
0.2b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite57.0ms

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 1) (/ (* 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)
19.0ms
(* (* 2.0 PI) u2)
29.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series2.2s

Counts
4 → 12
Calls
4 calls:
653.0ms
(fma (* (/ 1 1) (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
386.0ms
(pow (* -2.0 (log u1)) 0.5)
36.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify1.7s

Counts
87 → 87
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01801152
14631085
22174934
done5000921

prune525.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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×expm1-log1p-u exp-prod div-exp pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×exp-sum pow-prod-down sqr-pow
2×pow-to-exp log-pow *-commutative
1×cbrt-undiv unpow-prod-down rem-log-exp associate-*l/ div-inv rem-exp-log
Counts
4 → 94
Calls
4 calls:
31.0ms
(* (* 2.0 PI) u2)
1.0ms
(log (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5))
3.0ms
(exp (log (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)))
40.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.9s

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (* 2.0 PI) u2)
745.0ms
(log (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5))
633.0ms
(exp (log (fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)))
1.4s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.5s

Counts
106 → 106
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02121844
14771763
221941562
done50011541

prune698.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b
(* (* 2.0 PI) u2)
0.2b
(/ (* 1.0 (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))) 6.0)
0.5b
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite134.0ms

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:
17.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
21.0ms
(* (* 2.0 PI) u2)
45.0ms
(/ (* 1.0 (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))) 6.0)
40.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series2.6s

Counts
4 → 12
Calls
4 calls:
418.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
62.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (* 1.0 (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))) 6.0)
1.0s
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify2.3s

Counts
151 → 151
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02552872
17782193
236781573
done50011537

prune753.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes593.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02022
12720
22918
done2918

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.3s8000×body80valid
696.0ms8000×pre80true