Details

Time bar (total: 39.9s)

sample197.0ms

Algorithm
intervals
Results
51.0ms256×body80valid
9.0ms256×pre80true

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01819
13419
27119
315519
447219
5316119
done500019

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize70.0ms

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

rewrite234.0ms

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:
124.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
13.0ms
(pow (* -2.0 (log u1)) 0.5)
36.0ms
(* (* 2.0 PI) u2)
51.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.9s

Counts
4 → 12
Calls
4 calls:
878.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
529.0ms
(pow (* -2.0 (log u1)) 0.5)
81.0ms
(* (* 2.0 PI) u2)
1.4s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.2s

Counts
99 → 99
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02031408
15471350
225481230
done50001207

prune795.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

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
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×div-exp pow-prod-down pow-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv
Counts
4 → 84
Calls
4 calls:
88.0ms
(+ (* (* 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)
31.0ms
(* (* 2.0 PI) u2)
16.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series2.6s

Counts
4 → 12
Calls
4 calls:
861.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
479.0ms
(pow (* -2.0 (log u1)) 0.5)
76.0ms
(* (* 2.0 PI) u2)
1.2s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify2.0s

Counts
96 → 96
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01951363
14841321
222031224
done50011181

prune805.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite954.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
29×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-cbrt-cube
13×div-exp associate-/l*
10×prod-exp
9×pow1
7×associate-/r*
6×unpow-prod-down pow-exp sqr-pow
4×cbrt-undiv cbrt-unprod add-log-exp
3×pow-to-exp frac-2neg associate-*r* pow-prod-down clear-num div-inv
2×flip3-- associate-/r/ flip-- associate-/l/
1×div-sub associate-*l* *-commutative
Counts
4 → 119
Calls
4 calls:
37.0ms
(* (* 2.0 PI) u2)
29.0ms
(/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0))
20.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
860.0ms
(/ (- (* (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (* 1.0 1.0))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))

series4.0s

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* 2.0 PI) u2)
1.4s
(/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0))
1.3s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.2s
(/ (- (* (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (* 1.0 1.0))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify3.2s

Counts
131 → 131
Iterations

Useful iterations: done (3.2s)

IterNodesCost
03264201
18013893
237123521
done50013509

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite775.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
29×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-cbrt-cube
13×div-exp associate-/l*
10×prod-exp
9×pow1
7×associate-/r*
6×unpow-prod-down pow-exp sqr-pow
4×cbrt-undiv cbrt-unprod add-log-exp
3×pow-to-exp frac-2neg associate-*r* pow-prod-down clear-num div-inv
2×flip3-- associate-/r/ flip-- associate-/l/
1×div-sub associate-*l* *-commutative
Counts
4 → 119
Calls
4 calls:
49.0ms
(* (* 2.0 PI) u2)
32.0ms
(/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0))
19.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
666.0ms
(/ (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) (- (* (* (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (* 1.0 1.0)) (pow (cos (* (* 2.0 PI) u2)) 2)) (* 0.5 0.5)))

series4.3s

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (* 2.0 PI) u2)
1.4s
(/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0))
1.4s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.5s
(/ (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5) (- (* (* (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (* 1.0 1.0)) (pow (cos (* (* 2.0 PI) u2)) 2)) (* 0.5 0.5)))

simplify3.1s

Counts
131 → 131
Iterations

Useful iterations: done (3.1s)

IterNodesCost
03263946
18103875
239023522
done50013512

prune1.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes1.3s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01819
12419
done2419

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.4s8000×body80valid
295.0ms8000×pre80true