Details

Time bar (total: 29.4s)

sample146.0ms

Algorithm
intervals
Results
47.0ms256×body80valid
9.0ms256×pre80true

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
01819
13518
27218
315618
445018
5140718
done500018

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

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

rewrite126.0ms

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:
1.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
14.0ms
(pow (* -2.0 (log u1)) 0.5)
50.0ms
(* (* 2.0 PI) u2)
53.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.4s

Counts
4 → 12
Calls
4 calls:
762.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
441.0ms
(pow (* -2.0 (log u1)) 0.5)
41.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.8s

Counts
104 → 104
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01971340
14471286
214391166
done50001147

prune627.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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

rewrite55.0ms

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
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv frac-2neg associate-*l* clear-num *-commutative fma-udef div-inv
Counts
4 → 89
Calls
4 calls:
1.0ms
(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
20.0ms
(pow (* -2.0 (log u1)) 0.5)
19.0ms
(* (* 2.0 PI) u2)
10.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series2.4s

Counts
4 → 12
Calls
4 calls:
759.0ms
(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
409.0ms
(pow (* -2.0 (log u1)) 0.5)
60.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify3.4s

Counts
101 → 101
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01891291
13831246
211641146
341631127
done50001126

prune644.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×pow1
20×add-cbrt-cube
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×times-frac
12×associate-*r*
11×prod-exp
10×pow-prod-down
9×cbrt-unprod
6×sqrt-prod
5×unpow-prod-down associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-/r*
2×pow-to-exp pow-pow associate-*l* *-commutative
1×cbrt-undiv frac-2neg clear-num div-inv
Counts
4 → 108
Calls
4 calls:
14.0ms
(pow (* -2.0 (log u1)) 0.5)
105.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
10.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
33.0ms
(* (* 2.0 PI) (sqrt u2))

series2.2s

Counts
4 → 12
Calls
4 calls:
461.0ms
(pow (* -2.0 (log u1)) 0.5)
77.0ms
(* (* (* 2.0 PI) (sqrt u2)) (sqrt u2))
1.5s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
137.0ms
(* (* 2.0 PI) (sqrt u2))

simplify2.0s

Counts
120 → 120
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02131425
14801244
214961126
done50011110

prune583.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite215.0ms

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:
12.0ms
(pow (* -2.0 (log u1)) 0.5)
95.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
48.0ms
(* (* 2.0 PI) u2)
51.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.8s

Counts
4 → 12
Calls
4 calls:
396.0ms
(pow (* -2.0 (log u1)) 0.5)
1.3s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
47.0ms
(* (* 2.0 PI) u2)
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.9s

Counts
132 → 132
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02081857
14501623
214281494
done50011485

prune793.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes793.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02124
12824
done2824

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.9s8000×body80valid
214.0ms8000×pre80true