Details

Time bar (total: 34.0s)

sample118.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
6.0ms256×pre80true

simplify5.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
15019
227419
3328419
done500119

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (* (/ 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))

rewrite138.0ms

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:
78.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
7.0ms
(pow (* -2.0 (log u1)) 0.5)
21.0ms
(* (* 2.0 PI) u2)
28.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.4s

Counts
4 → 12
Calls
4 calls:
718.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
485.0ms
(pow (* -2.0 (log u1)) 0.5)
60.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
99 → 99
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02031408
112911346
done50001213

prune543.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize46.0ms

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

rewrite220.0ms

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×associate-*l/ 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 → 112
Calls
4 calls:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
131.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
35.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
31.0ms
(* (* 2.0 PI) u2)

series2.7s

Counts
4 → 12
Calls
4 calls:
425.0ms
(pow (* -2.0 (log u1)) 0.5)
1.1s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
50.0ms
(* (* 2.0 PI) u2)

simplify2.7s

Counts
124 → 124
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02001773
111151542
done50001413

prune708.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(* u2 PI)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 2 0.5)))
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b
(/ (- (* (cos (* 2.0 (* u2 PI))) (* (/ 1.0 (/ 6.0 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 2 0.5))))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

rewrite905.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log add-sqr-sqrt
31×times-frac
30×add-cube-cbrt *-un-lft-identity
29×associate-*l*
21×prod-exp
18×add-cbrt-cube
13×associate-*r*
9×div-exp unswap-sqr
8×pow-exp
6×pow1 sqr-pow
5×cbrt-unprod
4×pow-to-exp add-log-exp
3×cbrt-undiv associate-/r* *-commutative div-inv associate-/l*
2×unpow-prod-down flip3-- associate-*l/ associate-/r/ flip-- associate-/l/
1×frac-2neg div-sub pow-prod-down clear-num
Counts
4 → 132
Calls
4 calls:
7.0ms
(* u2 PI)
28.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 2 0.5)))
31.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
833.0ms
(/ (- (* (cos (* 2.0 (* u2 PI))) (* (/ 1.0 (/ 6.0 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 2 0.5))))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series3.3s

Counts
4 → 12
Calls
4 calls:
36.0ms
(* u2 PI)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 2 0.5)))
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s
(/ (- (* (cos (* 2.0 (* u2 PI))) (* (/ 1.0 (/ 6.0 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 2 0.5))))) (cos (* 2.0 (* u2 PI))))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify3.0s

Counts
144 → 144
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03264348
145074013
done50003723

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (pow (cos (* 2.0 (* u2 PI))) 2) (- (log u1))) 0.05555555555555555)
0.3b
(* (* 2.0 PI) u2)
0.3b
(* u2 PI)
0.3b
(/ (- (- 0.25 (* (* (pow (cos (* 2.0 (* u2 PI))) 2) (- (log u1))) 0.05555555555555555))) (- (* (* (cos (* (* 2.0 PI) u2)) (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5)) 0.16666666666666666) 0.5))

rewrite325.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
30×times-frac
23×add-exp-log
18×add-cbrt-cube
13×pow1
12×distribute-lft-neg-in distribute-rgt-neg-in
11×prod-exp
10×associate-/l*
9×associate-*r*
7×cbrt-unprod
5×associate-*l* pow-prod-down
4×neg-mul-1 add-log-exp
3×associate-/r* *-commutative
2×flip3-- associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv distribute-lft-neg-out neg-sub0 pow-to-exp frac-2neg div-sub distribute-frac-neg div-exp pow-exp clear-num distribute-rgt-neg-out div-inv unswap-sqr
Counts
4 → 117
Calls
4 calls:
76.0ms
(* (* (pow (cos (* 2.0 (* u2 PI))) 2) (- (log u1))) 0.05555555555555555)
27.0ms
(* (* 2.0 PI) u2)
7.0ms
(* u2 PI)
207.0ms
(/ (- (- 0.25 (* (* (pow (cos (* 2.0 (* u2 PI))) 2) (- (log u1))) 0.05555555555555555))) (- (* (* (cos (* (* 2.0 PI) u2)) (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5)) 0.16666666666666666) 0.5))

series1.3s

Counts
4 → 12
Calls
4 calls:
159.0ms
(* (* (pow (cos (* 2.0 (* u2 PI))) 2) (- (log u1))) 0.05555555555555555)
44.0ms
(* (* 2.0 PI) u2)
31.0ms
(* u2 PI)
1.1s
(/ (- (- 0.25 (* (* (pow (cos (* 2.0 (* u2 PI))) 2) (- (log u1))) 0.05555555555555555))) (- (* (* (cos (* (* 2.0 PI) u2)) (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (- (log u1)) 1.0))) 0.5)) 0.16666666666666666) 0.5))

simplify2.7s

Counts
129 → 129
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02985322
137155203
done50004964

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes423.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02025
12725
done2725

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.0s8000×body80valid
200.0ms8000×pre80true