Details

Time bar (total: 28.7s)

sample155.0ms

Algorithm
intervals
Results
51.0ms256×body80valid
9.0ms256×pre80true

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (67.0ms)

IterNodesCost
01819
13518
27218
315618
445018
5140718
done500018

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

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

rewrite82.0ms

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)
27.0ms
(* (* 2.0 PI) u2)
44.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.4s

Counts
4 → 12
Calls
4 calls:
706.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
486.0ms
(pow (* -2.0 (log u1)) 0.5)
73.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
104 → 104
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01971340
14471286
214391166
done50001147

prune490.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))

rewrite171.0ms

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:
10.0ms
(pow (* -2.0 (log u1)) 0.5)
81.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
24.0ms
(* (* 2.0 PI) u2)
47.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series3.0s

Counts
4 → 12
Calls
4 calls:
446.0ms
(pow (* -2.0 (log u1)) 0.5)
1.2s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
74.0ms
(* (* 2.0 PI) u2)
1.3s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify2.0s

Counts
132 → 132
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02081857
14501623
214281494
done50011485

prune806.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
0.1b
(* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))
0.2b
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (- 0.16666666666666666 (* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))))
0.3b
(* (pow u2 2) (pow PI 2))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
58×prod-exp
44×pow-exp
33×add-sqr-sqrt
26×pow-to-exp
18×unswap-sqr
16×unpow-prod-down associate-*l*
14×add-cube-cbrt *-un-lft-identity
13×add-cbrt-cube sqr-pow
12×associate-*r*
10×unpow2
7×pow1
6×prod-diff
5×distribute-rgt-in distribute-lft-in cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow pow-prod-down *-commutative
2×sub-neg pow-pow associate-*r/
1×flip3-- flip--
Counts
4 → 152
Calls
4 calls:
21.0ms
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
32.0ms
(* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))
58.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (- 0.16666666666666666 (* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))))
48.0ms
(* (pow u2 2) (pow PI 2))

series3.2s

Counts
4 → 12
Calls
4 calls:
1.4s
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
97.0ms
(* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))
1.7s
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (- 0.16666666666666666 (* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))))
56.0ms
(* (pow u2 2) (pow PI 2))

simplify1.6s

Counts
164 → 164
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02752982
16362753
219252422
done50002384

prune715.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
0.6b
(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log
24×prod-exp
23×add-cbrt-cube
19×sqrt-prod
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×associate-*l*
15×times-frac
14×pow1
9×cbrt-unprod
6×div-exp pow-exp associate-/r*
5×pow-prod-down
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×cbrt-undiv pow-to-exp pow-unpow
2×pow-pow sqrt-div associate-*l/ *-commutative div-inv
1×unpow-prod-down frac-2neg clear-num associate-/l/ associate-/l* sqr-pow
Counts
4 → 110
Calls
4 calls:
14.0ms
(pow (* -2.0 (log u1)) 0.5)
32.0ms
(* (* 2.0 PI) u2)
68.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
58.0ms
(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

series3.1s

Counts
4 → 12
Calls
4 calls:
447.0ms
(pow (* -2.0 (log u1)) 0.5)
75.0ms
(* (* 2.0 PI) u2)
1.2s
(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
1.4s
(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

simplify1.3s

Counts
122 → 122
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02291900
15161728
217681579
done50001570

prune766.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes496.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01924
12424
done2424

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.9s8000×body80valid
231.0ms8000×pre80true