Details

Time bar (total: 17.2s)

sample295.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
5.0ms256×pre80true

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
01819
13518
27118
315318
440318
5132318
done500018

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

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)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite26.0ms

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)
2.0ms
(pow (* -2.0 (log u1)) 0.5)
7.0ms
(* (* 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:
473.0ms
(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
253.0ms
(pow (* -2.0 (log u1)) 0.5)
31.0ms
(* (* 2.0 PI) u2)
694.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify812.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (169.0ms)

IterNodesCost
01971340
14541286
215241166
done50001166

prune361.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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:
5.0ms
(pow (* -2.0 (log u1)) 0.5)
6.0ms
(* (* 2.0 PI) u2)
13.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
26.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

series1.8s

Counts
4 → 12
Calls
4 calls:
265.0ms
(pow (* -2.0 (log u1)) 0.5)
37.0ms
(* (* 2.0 PI) u2)
722.0ms
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
739.0ms
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

simplify942.0ms

Counts
132 → 132
Iterations

Useful iterations: 2 (153.0ms)

IterNodesCost
02081857
14551623
214491494
done50011494

prune479.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
0.2b
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666)
0.2b
(* (* 2.0 PI) u2)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
33×prod-exp
32×pow-exp
14×pow-to-exp
11×add-sqr-sqrt add-cbrt-cube
10×pow1
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l*
4×expm1-log1p-u pow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×pow-unpow sqr-pow
2×unpow-prod-down pow-pow *-commutative unswap-sqr
1×fma-udef
Counts
4 → 90
Calls
4 calls:
0.0ms
(fma (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2)) 0.5)
4.0ms
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
7.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666)
6.0ms
(* (* 2.0 PI) u2)

series2.1s

Counts
4 → 12
Calls
4 calls:
462.0ms
(fma (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666) (cos (* (* 2.0 PI) u2)) 0.5)
871.0ms
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
692.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) 0.16666666666666666)
37.0ms
(* (* 2.0 PI) u2)

simplify814.0ms

Counts
102 → 102
Iterations

Useful iterations: done (811.0ms)

IterNodesCost
02001543
14571444
213641333
done50001323

prune487.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2))
0.2b
(* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2))) 0.16666666666666666)
0.2b
(* (* 2.0 PI) u2)
0.5b
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
877×prod-exp
840×add-exp-log
784×pow-exp
343×pow-to-exp
22×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
16×add-cbrt-cube
13×pow-unpow
12×pow1
11×associate-*r*
9×times-frac sqr-pow
7×associate-*l* cbrt-unprod
6×pow-prod-down
5×unpow-prod-down swap-sqr unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative
2×pow-pow
1×pow2 pow-sqr pow-prod-up div-inv
Counts
4 → 398
Calls
4 calls:
6.0ms
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2))
24.0ms
(* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2))) 0.16666666666666666)
7.0ms
(* (* 2.0 PI) u2)
13.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)))

series2.3s

Counts
4 → 12
Calls
4 calls:
883.0ms
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2))
724.0ms
(* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2))) 0.16666666666666666)
32.0ms
(* (* 2.0 PI) u2)
672.0ms
(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) (/ 0.5 2)))

simplify874.0ms

Counts
410 → 410
Iterations

Useful iterations: 2 (289.0ms)

IterNodesCost
029711420
17475414
219675041
done50005041

prune458.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes311.0ms

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

sample926.0ms

Algorithm
intervals
Results
638.0ms8000×body80valid
135.0ms8000×pre80true