Details

Time bar (total: 35.7s)

sample171.0ms

Algorithm
intervals
Results
42.0ms256×body80valid
7.0ms256×pre80true

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
018628
135603
272603
3159603
4483603
53177603
done5000603

prune20.0ms

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))

rewrite141.0ms

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×expm1-log1p-u div-exp pow-prod-down log1p-expm1-u unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative sum-log fma-def flip3-+ associate-*l/ flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
95.0ms
(+ (* (* (/ 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)
13.0ms
(* (* 2.0 PI) u2)
20.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
643.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
373.0ms
(pow (* -2.0 (log u1)) 0.5)
50.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.6s

Counts
108 → 108
Iterations

Useful iterations: done (2.6s)

IterNodesCost
021449757
157547007
2266946396
done500046026

prune778.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×times-frac
12×pow1
11×add-cbrt-cube
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp log1p-expm1-u
3×pow-unpow associate-/r* associate-*r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative clear-num sum-log fma-def frac-2neg flip3-+ associate-*l* *-commutative flip-+ div-inv
Counts
4 → 93
Calls
4 calls:
78.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
9.0ms
(pow (* -2.0 (log u1)) 0.5)
13.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
27.0ms
(* (* 2.0 PI) u2)

series2.3s

Counts
4 → 12
Calls
4 calls:
675.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
446.0ms
(pow (* -2.0 (log u1)) 0.5)
1.1s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
62.0ms
(* (* 2.0 PI) u2)

simplify2.0s

Counts
105 → 105
Iterations

Useful iterations: done (2.0s)

IterNodesCost
020650197
151147723
2224547498
done500047073

prune957.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
666×add-exp-log
500×prod-exp
96×add-cbrt-cube
89×div-exp
88×pow-exp
60×cbrt-unprod
45×add-sqr-sqrt
44×pow-to-exp
43×pow1
34×times-frac
29×*-un-lft-identity add-cube-cbrt
27×associate-*l*
17×pow-prod-down
11×cbrt-undiv associate-*r* associate-*l/
8×unswap-sqr
6×sqr-pow
4×expm1-log1p-u pow-sqr pow-prod-up log1p-expm1-u associate-/l* add-log-exp difference-of-squares
3×associate-/r* *-commutative div-inv
2×unpow-prod-down pow-plus flip3-- associate-/r/ flip-- associate-/l/
1×pow2 frac-times clear-num frac-2neg div-sub swap-sqr associate-*r/
Counts
4 → 271
Calls
4 calls:
18.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
27.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s
(/ (- (* (* (* (/ 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))
390.0ms
(* (* (* (/ 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))))

series4.1s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.2s
(/ (- (* (* (* (/ 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))
791.0ms
(* (* (* (/ 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))))

simplify3.2s

Counts
283 → 283
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0374234324
11203194042
done5001181584

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b
(/ (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2))) 6.0)
0.3b
(* (* 2.0 PI) u2)
0.5b
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
94×add-exp-log
52×prod-exp
34×pow-exp
22×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
17×pow-to-exp div-exp
16×add-cbrt-cube
13×pow-unpow
12×pow1 times-frac
9×sqr-pow
8×associate-*r*
6×associate-*l*
5×unpow-prod-down swap-sqr pow-prod-down cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×cbrt-undiv pow-pow *-commutative div-inv
1×pow2 clear-num frac-2neg pow-sqr pow-prod-up associate-/l*
Counts
4 → 137
Calls
4 calls:
13.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
18.0ms
(/ (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2))) 6.0)
13.0ms
(* (* 2.0 PI) u2)
30.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series2.6s

Counts
4 → 12
Calls
4 calls:
423.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
1.1s
(/ (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2))) 6.0)
59.0ms
(* (* 2.0 PI) u2)
968.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify2.7s

Counts
149 → 149
Iterations

Useful iterations: done (2.7s)

IterNodesCost
023574246
163965763
2326963417
done500260384

prune986.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes1.2s

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 (2.0ms)

IterNodesCost
020768
126768
done26768

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.7s8000×body80valid
352.0ms8000×pre80true