Details

Time bar (total: 15.0s)

sample292.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
5.0ms256×pre80true

simplify752.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01819
13518
27118
315418
442918
5143618
done500018

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
0.2b
(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))

rewrite25.0ms

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
5×cbrt-unprod
4×expm1-log1p-u div-exp pow-prod-down log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv associate-*l/ fma-udef div-inv
Counts
4 → 92
Calls
4 calls:
0.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
3.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
12.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts
4 → 12
Calls
4 calls:
463.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
266.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
699.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify602.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (143.0ms)

IterNodesCost
01971340
14611286
217531166
done50001166

prune348.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv frac-2neg associate-*l* clear-num *-commutative fma-udef div-inv
Counts
4 → 89
Calls
4 calls:
0.0ms
(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
2.0ms
(pow (* -2.0 (log u1)) 0.5)
3.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
6.0ms
(* (* 2.0 PI) u2)

series1.4s

Counts
4 → 12
Calls
4 calls:
457.0ms
(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
265.0ms
(pow (* -2.0 (log u1)) 0.5)
685.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
35.0ms
(* (* 2.0 PI) u2)

simplify505.0ms

Counts
101 → 101
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
01891291
13881246
214261146
done50011146

prune365.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
23×prod-exp
22×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
11×pow1 times-frac
9×rem-log-exp
8×div-exp associate-*r* pow-exp
5×cbrt-unprod
4×expm1-log1p-u pow-to-exp exp-prod log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down associate-*l/ sqr-pow
2×log-div log-prod log-pow *-commutative
1×cbrt-undiv unpow-prod-down exp-diff exp-sum div-inv rem-exp-log
Counts
4 → 100
Calls
4 calls:
6.0ms
(* (* 2.0 PI) u2)
6.0ms
(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
13.0ms
(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
14.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* 2.0 PI) u2)
835.0ms
(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
707.0ms
(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
692.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify559.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
01841323
14101243
214741129
done50001129

prune429.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log
33×add-sqr-sqrt
32×associate-*l*
30×sqrt-prod
25×prod-exp
22×add-cube-cbrt *-un-lft-identity
20×times-frac
13×sqrt-div
12×pow1
11×add-cbrt-cube
10×associate-*l/
6×log-div rem-log-exp associate-*r* pow-exp unswap-sqr
5×exp-prod
4×expm1-log1p-u log-pow cbrt-unprod log1p-expm1-u add-log-exp sqr-pow
3×frac-times pow-to-exp exp-diff associate-*r/ pow-prod-down
2×log-prod *-commutative div-inv
1×unpow-prod-down exp-sum rem-exp-log
Counts
4 → 121
Calls
4 calls:
26.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
24.0ms
(log (* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))))
15.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
66.0ms
(exp (log (* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
750.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
927.0ms
(log (* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))))
868.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
766.0ms
(exp (log (* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))))

simplify484.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
01882313
13831863
212451708
done50001708

prune545.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes326.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01820
12220
done2220

end0.0ms

sample956.0ms

Algorithm
intervals
Results
668.0ms8000×body80valid
132.0ms8000×pre80true