Details

Time bar (total: 25.0s)

sample92.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
5.0ms256×pre80true

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
01819
13518
27218
315918
448318
5314018
done500118

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

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)
0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (* 2.0 PI) u2)
0.3b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite115.0ms

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:
1.0ms
(fma (* (/ 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)
57.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
703.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
411.0ms
(pow (* -2.0 (log u1)) 0.5)
65.0ms
(* (* 2.0 PI) u2)
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts
104 → 104
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01971340
14941292
223001170
done50001151

prune543.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* 1 (/ (* 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
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.2b
(* (* 2.0 PI) u2)

rewrite59.0ms

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
5×div-exp
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×unpow-prod-down frac-2neg associate-*l* clear-num *-commutative fma-udef div-inv associate-/l* sqr-pow
Counts
4 → 75
Calls
4 calls:
1.0ms
(fma (* 1 (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
13.0ms
(pow (* -2.0 (log u1)) 0.5)
23.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
18.0ms
(* (* 2.0 PI) u2)

series2.1s

Counts
4 → 12
Calls
4 calls:
665.0ms
(fma (* 1 (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
385.0ms
(pow (* -2.0 (log u1)) 0.5)
1.0s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
50.0ms
(* (* 2.0 PI) u2)

simplify1.9s

Counts
87 → 87
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01791126
14681059
22333940
done5000927

prune631.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.2b
(* (* 2.0 PI) u2)
1.0b
(expm1 (fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5))

rewrite84.0ms

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
5×div-exp log1p-expm1-u
4×expm1-log1p-u pow-prod-down pow-exp cbrt-unprod add-log-exp
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×unpow-prod-down expm1-log1p frac-2neg associate-*l* clear-num *-commutative div-inv associate-/l* expm1-udef sqr-pow
Counts
4 → 76
Calls
4 calls:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
29.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
36.0ms
(* (* 2.0 PI) u2)
1.0ms
(expm1 (fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
390.0ms
(pow (* -2.0 (log u1)) 0.5)
1.0s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
41.0ms
(* (* 2.0 PI) u2)
810.0ms
(expm1 (fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5))

simplify2.0s

Counts
88 → 88
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01861139
14811091
22199964
done5000949

prune556.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) 0.5)
0.2b
(* (sqrt (/ 1.0 6.0)) (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)

rewrite214.0ms

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:
13.0ms
(pow (* -2.0 (log u1)) 0.5)
54.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
119.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
19.0ms
(* (* 2.0 PI) u2)

series2.5s

Counts
4 → 12
Calls
4 calls:
367.0ms
(pow (* -2.0 (log u1)) 0.5)
1.0s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
1.0s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
53.0ms
(* (* 2.0 PI) u2)

simplify1.6s

Counts
132 → 132
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02081857
14941770
221581500
done50001489

prune800.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes698.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01920
12320
done2320

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.4s8000×body80valid
275.0ms8000×pre80true