Details

Time bar (total: 29.5s)

sample127.0ms

Algorithm
intervals
Results
31.0ms256×body80valid
6.0ms256×pre80true

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01819
13419
27119
315519
447219
5316119
done500019

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

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)
0.2b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite195.0ms

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:
111.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
15.0ms
(pow (* -2.0 (log u1)) 0.5)
17.0ms
(* (* 2.0 PI) u2)
42.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
677.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
405.0ms
(pow (* -2.0 (log u1)) 0.5)
46.0ms
(* (* 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
15471350
225481230
done50001207

prune519.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize42.0ms

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

rewrite181.0ms

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:
101.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
12.0ms
(pow (* -2.0 (log u1)) 0.5)
35.0ms
(* (* 2.0 PI) u2)
27.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series2.1s

Counts
4 → 12
Calls
4 calls:
666.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
346.0ms
(pow (* -2.0 (log u1)) 0.5)
47.0ms
(* (* 2.0 PI) u2)
1.0s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify1.5s

Counts
96 → 96
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01951363
14841321
222031224
done50011181

prune509.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) u2)
0.2b
(log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
0.2b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.3b
(exp (log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×times-frac
11×pow1 add-cbrt-cube
6×log-prod
5×associate-/l*
4×unpow-prod-down log-div exp-prod div-exp prod-exp add-log-exp sqr-pow
3×associate-*r* exp-sum pow-prod-down associate-/r* cbrt-unprod
2×flip3-+ exp-diff pow-exp log-pow flip-+
1×cbrt-undiv pow-to-exp frac-2neg rem-log-exp associate-*l* clear-num *-commutative div-inv rem-exp-log
Counts
4 → 87
Calls
4 calls:
18.0ms
(* (* 2.0 PI) u2)
70.0ms
(log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
15.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
138.0ms
(exp (log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))

series2.8s

Counts
4 → 12
Calls
4 calls:
382.0ms
(* (* 2.0 PI) u2)
761.0ms
(log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
982.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
668.0ms
(exp (log (+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))

simplify1.2s

Counts
99 → 99
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02172011
14581932
219171724
done50011682

prune584.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b
(* (/ 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))) (+ (- 0.5) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))))
0.7b
(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

rewrite459.0ms

Algorithm
rewrite-expression-head
Rules
116×add-exp-log
68×prod-exp
38×add-sqr-sqrt add-cbrt-cube
27×associate-*l*
26×pow-exp
22×add-cube-cbrt *-un-lft-identity times-frac
18×cbrt-unprod
16×div-exp
13×associate-*r*
12×pow1
11×associate-*l/
9×pow-to-exp
8×unswap-sqr
7×sqr-pow
4×cbrt-undiv pow-prod-down add-log-exp rem-cube-cbrt
3×unpow-prod-down pow-unpow *-commutative
2×frac-times pow-pow flip3-+ associate-*r/ flip-+ div-inv
1×cube-div distribute-rgt-in cube-mult distribute-lft-in unpow3 cube-prod
Counts
4 → 150
Calls
4 calls:
29.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
24.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
298.0ms
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (+ (- 0.5) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))))
95.0ms
(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

series4.0s

Counts
4 → 12
Calls
4 calls:
974.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
932.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.3s
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (+ (- 0.5) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))))
786.0ms
(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

simplify4.3s

Counts
162 → 162
Iterations

Useful iterations: 2 (803.0ms)

IterNodesCost
02684127
18013771
248983301
done50023301

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes692.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01819
12419
done2419

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.3s8000×body80valid
775.0ms8000×pre80true