Details

Time bar (total: 51.6s)

sample186.0ms

Algorithm
intervals
Results
49.0ms256×body80valid
9.0ms256×pre80true

simplify8.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
018628
134628
269628
3145628
4385628
51534628
done5000628

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (/ 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)
0.3b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×*-un-lft-identity add-cbrt-cube associate-*l* prod-exp add-cube-cbrt
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 sum-log flip3-+ associate-*l/ flip-+ div-inv
Counts
4 → 87
Calls
4 calls:
54.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
11.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
21.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
693.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
447.0ms
(pow (* -2.0 (log u1)) 0.5)
71.0ms
(* (* 2.0 PI) u2)
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.6s

Counts
99 → 99
Iterations

Useful iterations: done (2.6s)

IterNodesCost
020646239
155543839
2183443278
done500142908

prune703.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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)

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt add-exp-log
33×associate-*l*
30×sqrt-prod
23×*-un-lft-identity add-cube-cbrt
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:
10.0ms
(pow (* -2.0 (log u1)) 0.5)
55.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
21.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
23.0ms
(* (* 2.0 PI) u2)

series2.8s

Counts
4 → 12
Calls
4 calls:
419.0ms
(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)))
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
73.0ms
(* (* 2.0 PI) u2)

simplify2.3s

Counts
124 → 124
Iterations

Useful iterations: done (2.3s)

IterNodesCost
020059190
148356719
2143754599
done500054269

prune893.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (cos (* (* 2.0 PI) u2))) 0.5)
0.3b
(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
149×add-exp-log
98×prod-exp
38×pow-exp
23×add-cbrt-cube
22×add-sqr-sqrt
20×div-exp
19×pow-to-exp
15×associate-*l*
14×*-un-lft-identity add-cube-cbrt
13×associate-*r*
11×times-frac
10×cbrt-unprod
9×pow1
6×add-log-exp
4×unswap-sqr sqr-pow
3×pow-prod-down associate-*l/ *-commutative
2×cbrt-undiv unpow-prod-down
1×+-commutative sum-log flip3-+ flip-+ div-inv
Counts
4 → 124
Calls
4 calls:
157.0ms
(+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (cos (* (* 2.0 PI) u2))) 0.5)
51.0ms
(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
27.0ms
(* (* 2.0 PI) u2)
36.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series3.0s

Counts
4 → 12
Calls
4 calls:
669.0ms
(+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (cos (* (* 2.0 PI) u2))) 0.5)
1.1s
(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
53.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify3.4s

Counts
136 → 136
Iterations

Useful iterations: done (3.4s)

IterNodesCost
023978977
161868699
2195968178
done500167358

prune842.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize215.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* (/ 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)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* (* 0.5 0.5) 0.5)) (+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))))
0.6b
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))
0.6b
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

rewrite4.7s

Algorithm
rewrite-expression-head
Rules
1246×add-exp-log
960×prod-exp
166×add-cbrt-cube
161×div-exp
160×pow-exp
112×cbrt-unprod
82×pow1
80×pow-to-exp
54×associate-*l/
34×pow-prod-down
17×cbrt-undiv
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac frac-add
9×add-log-exp
8×pow3 associate-/r/ pow-sqr pow-prod-up
6×frac-times flip3-- associate-*r/ flip--
4×pow-plus sum-cubes associate-/l*
3×associate-/r* flip3-+ flip-+
2×pow2 associate-+r+ sum-log swap-sqr associate-*r* associate-*l* *-commutative associate-/l/
1×+-commutative clear-num associate-+r- sub-neg frac-2neg diff-log div-inv
Counts
4 → 352
Calls
4 calls:
341.0ms
(+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
3.4s
(/ (+ (* (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* (* 0.5 0.5) 0.5)) (+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))))
420.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))
434.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

series4.2s

Counts
4 → 12
Calls
4 calls:
783.0ms
(+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
1.8s
(/ (+ (* (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* (* 0.5 0.5) 0.5)) (+ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))))
890.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))
718.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

simplify10.1s

Counts
364 → 364
Iterations

Useful iterations: done (10.0s)

IterNodesCost
0409368589
11164296511
24290276431
done5000260851

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
020708
127708
done27708

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.5s8000×body80valid
280.0ms8000×pre80true