Details

Time bar (total: 29.8s)

sample163.0ms

Algorithm
intervals
Results
53.0ms256×body80valid
9.0ms256×pre80true

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 1 (302.0ms)

IterNodesCost
01819
13518
27218
315918
448318
5314018
done500118

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (* (/ 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)
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite159.0ms

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:
85.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
33.0ms
(* (* 2.0 PI) u2)
29.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.1s

Counts
4 → 12
Calls
4 calls:
641.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
441.0ms
(pow (* -2.0 (log u1)) 0.5)
42.0ms
(* (* 2.0 PI) u2)
955.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.8s

Counts
108 → 108
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02111496
15651422
226081301
done50001292

prune637.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize27.0ms

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

rewrite175.0ms

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:
7.0ms
(pow (* -2.0 (log u1)) 0.5)
92.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
19.0ms
(* (* 2.0 PI) u2)
53.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.5s

Counts
4 → 12
Calls
4 calls:
405.0ms
(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)))
59.0ms
(* (* 2.0 PI) u2)
1.0s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.5s

Counts
132 → 132
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02081857
14921770
221331512
done50011489

prune859.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)))
0.3b
(* (* 2.0 PI) u2)
0.4b
(* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))
0.4b
(expm1 (log1p (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×add-sqr-sqrt
16×associate-*r*
14×add-cbrt-cube
13×add-cube-cbrt *-un-lft-identity prod-exp
11×times-frac
9×pow1
6×associate-*l*
5×expm1-log1p-u cbrt-unprod
4×div-exp pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down sqr-pow
2×pow-to-exp *-commutative
1×cbrt-undiv unpow-prod-down log1p-udef expm1-log1p log1p-expm1 associate-*r/ div-inv expm1-udef
Counts
4 → 85
Calls
4 calls:
0.0ms
(log1p (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)))
24.0ms
(* (* 2.0 PI) u2)
45.0ms
(* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))
1.0ms
(expm1 (log1p (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))))

series4.3s

Counts
4 → 12
Calls
4 calls:
1.3s
(log1p (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)))
36.0ms
(* (* 2.0 PI) u2)
1.6s
(* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))
1.4s
(expm1 (log1p (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))))

simplify1.9s

Counts
97 → 97
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01821268
14291197
221321071
done50001062

prune547.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 2.0 PI) u2)
0.4b
(* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))
0.6b
(cbrt (pow (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)) 3))
0.7b
(pow (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)) 3)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
23×add-sqr-sqrt prod-exp
20×add-cbrt-cube
17×pow-exp
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac
10×pow1
8×cbrt-prod div-exp
7×cbrt-unprod
6×associate-*l*
5×pow-to-exp sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×unpow-prod-down pow-unpow associate-*r/ pow-prod-down rem-cube-cbrt
2×cbrt-undiv cube-div cube-mult unpow3 cube-prod *-commutative
1×cbrt-div pow-pow pow1/3 rem-cbrt-cube div-inv
Counts
4 → 115
Calls
4 calls:
36.0ms
(* (* 2.0 PI) u2)
45.0ms
(* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))
11.0ms
(cbrt (pow (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)) 3))
35.0ms
(pow (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)) 3)

series3.5s

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* 2.0 PI) u2)
1.1s
(* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))
1.1s
(cbrt (pow (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)) 3))
1.2s
(pow (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)) 3)

simplify2.5s

Counts
127 → 127
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02221782
15661581
231131462
done50021460

prune672.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes602.0ms

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
02025
12725
done2725

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.8s8000×body80valid
220.0ms8000×pre80true