Details

Time bar (total: 26.8s)

sample119.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
5.0ms256×pre80true

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
01819
13518
27218
315618
445018
5140718
done500018

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

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))

rewrite128.0ms

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×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 fma-def flip3-+ associate-*l/ sum-log flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
69.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
8.0ms
(pow (* -2.0 (log u1)) 0.5)
18.0ms
(* (* 2.0 PI) u2)
25.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.4s

Counts
4 → 12
Calls
4 calls:
1.0s
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
330.0ms
(pow (* -2.0 (log u1)) 0.5)
57.0ms
(* (* 2.0 PI) u2)
997.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
108 → 108
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02111496
15151416
216951295
done50011265

prune569.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize34.0ms

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

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
14×add-cbrt-cube
12×pow1
9×prod-exp
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×div-exp
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod log1p-expm1-u
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×+-commutative unpow-prod-down fma-def frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv associate-/l* sqr-pow
Counts
4 → 79
Calls
4 calls:
50.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
18.0ms
(* (* 2.0 PI) u2)
23.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series2.0s

Counts
4 → 12
Calls
4 calls:
714.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
380.0ms
(pow (* -2.0 (log u1)) 0.5)
62.0ms
(* (* 2.0 PI) u2)
868.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify1.4s

Counts
91 → 91
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01921256
14651191
215781059
done50011029

prune513.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize40.0ms

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

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log add-sqr-sqrt
33×associate-*l*
30×sqrt-prod
23×add-cube-cbrt *-un-lft-identity
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×expm1-log1p-u associate-*l/ log1p-expm1-u 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 → 120
Calls
4 calls:
6.0ms
(pow (* -2.0 (log u1)) 0.5)
75.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
36.0ms
(* (* 2.0 PI) u2)
56.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.6s

Counts
4 → 12
Calls
4 calls:
380.0ms
(pow (* -2.0 (log u1)) 0.5)
1.1s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
65.0ms
(* (* 2.0 PI) u2)
1.0s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
132 → 132
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02081857
14501623
214281494
done50011485

prune750.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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))
1.0b
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

rewrite77.0ms

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 log1p-expm1-u
4×expm1-log1p-u div-exp pow-prod-down add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv expm1-log1p associate-*l/ div-inv expm1-udef
Counts
4 → 93
Calls
4 calls:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
25.0ms
(* (* 2.0 PI) u2)
32.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0ms
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

series2.4s

Counts
4 → 12
Calls
4 calls:
312.0ms
(pow (* -2.0 (log u1)) 0.5)
40.0ms
(* (* 2.0 PI) u2)
968.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

simplify3.7s

Counts
105 → 105
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01851218
14131159
212971053
346891044
done50001044

prune481.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes330.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02021
12621
done2621

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8000×body80valid
197.0ms8000×pre80true