Details

Time bar (total: 26.6s)

sample254.0ms

Algorithm
intervals
Results
127.0ms256×body80valid
11.0ms256×pre80true

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (75.0ms)

IterNodesCost
01819
13518
27218
315618
445018
5140718
done500018

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)
0.3b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite80.0ms

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)
12.0ms
(pow (* -2.0 (log u1)) 0.5)
28.0ms
(* (* 2.0 PI) u2)
33.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
727.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
344.0ms
(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))

simplify1.7s

Counts
104 → 104
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01971340
14471286
214391166
done50001147

prune537.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

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)
85.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
42.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
26.0ms
(* (* 2.0 PI) u2)

series2.6s

Counts
4 → 12
Calls
4 calls:
457.0ms
(pow (* -2.0 (log u1)) 0.5)
1.2s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
958.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
47.0ms
(* (* 2.0 PI) u2)

simplify1.9s

Counts
132 → 132
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02081857
14501623
214361494
done50001485

prune843.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite69.0ms

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:
0.0ms
(fma (/ (* 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)
32.0ms
(* (* 2.0 PI) u2)
28.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series2.3s

Counts
4 → 12
Calls
4 calls:
673.0ms
(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
433.0ms
(pow (* -2.0 (log u1)) 0.5)
38.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify1.4s

Counts
87 → 87
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01781100
13971053
21324930
done5001911

prune428.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (cos (* (* 2.0 PI) u2)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
149×add-exp-log
98×prod-exp
38×pow-exp
23×add-cbrt-cube
22×add-sqr-sqrt
20×div-exp
19×pow-to-exp
15×associate-*l*
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
11×times-frac
10×cbrt-unprod
9×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-prod-down associate-*l/ *-commutative
2×cbrt-undiv unpow-prod-down
1×fma-udef div-inv
Counts
4 → 129
Calls
4 calls:
1.0ms
(fma (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (cos (* (* 2.0 PI) u2)) 0.5)
29.0ms
(* (* 2.0 PI) u2)
77.0ms
(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
37.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series3.3s

Counts
4 → 12
Calls
4 calls:
664.0ms
(fma (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2))) (cos (* (* 2.0 PI) u2)) 0.5)
51.0ms
(* (* 2.0 PI) u2)
1.5s
(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify1.6s

Counts
141 → 141
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02302950
15312304
217732044
done50002018

prune567.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes362.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01924
12424
done2424

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.3s8000×body80valid
422.0ms8000×pre80true