Details

Time bar (total: 27.1s)

sample183.0ms

Algorithm
intervals
Results
39.0ms256×body80valid
7.0ms256×pre80true

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
01819
13518
27218
315918
448318
5314018
done500118

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

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)
0.1b
(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))

rewrite71.0ms

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)
7.0ms
(pow (* -2.0 (log u1)) 0.5)
33.0ms
(* (* 2.0 PI) u2)
26.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

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)
394.0ms
(pow (* -2.0 (log u1)) 0.5)
57.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.0s

Counts
104 → 104
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01971340
14941292
223001170
done50001151

prune542.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)
0.3b
(* (* 2.0 PI) u2)

rewrite63.0ms

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)
12.0ms
(pow (* -2.0 (log u1)) 0.5)
28.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
18.0ms
(* (* 2.0 PI) u2)

series2.3s

Counts
4 → 12
Calls
4 calls:
712.0ms
(fma (* 1 (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
414.0ms
(pow (* -2.0 (log u1)) 0.5)
1.1s
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
74.0ms
(* (* 2.0 PI) u2)

simplify1.9s

Counts
87 → 87
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01791126
14681059
22333940
done5000927

prune564.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* 1 (* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
0.3b
(* (* 2.0 PI) u2)
0.3b
(* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))

rewrite86.0ms

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 associate-*r*
4×expm1-log1p-u associate-*l* 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:
1.0ms
(fma (* 1 (* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))) (cos (* (* 2.0 PI) u2)) 0.5)
19.0ms
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
24.0ms
(* (* 2.0 PI) u2)
37.0ms
(* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))

series3.2s

Counts
4 → 12
Calls
4 calls:
702.0ms
(fma (* 1 (* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))) (cos (* (* 2.0 PI) u2)) 0.5)
1.3s
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
62.0ms
(* (* 2.0 PI) u2)
1.1s
(* 0.16666666666666666 (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01991570
15081458
221071342
done50001323

prune588.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
0.2b
(* (sqrt 0.16666666666666666) (* (sqrt 0.16666666666666666) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)))
0.3b
(* (* 2.0 PI) u2)
0.3b
(* (sqrt 0.16666666666666666) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
88×add-exp-log
67×prod-exp
48×pow-exp
21×pow-to-exp
17×add-sqr-sqrt
16×add-cbrt-cube
13×associate-*l*
12×pow1
11×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×sqrt-prod
7×cbrt-unprod
5×pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-unpow *-commutative
2×unpow-prod-down pow-pow
Counts
4 → 118
Calls
4 calls:
10.0ms
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
61.0ms
(* (sqrt 0.16666666666666666) (* (sqrt 0.16666666666666666) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)))
18.0ms
(* (* 2.0 PI) u2)
30.0ms
(* (sqrt 0.16666666666666666) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))

series3.6s

Counts
4 → 12
Calls
4 calls:
1.4s
(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
1.1s
(* (sqrt 0.16666666666666666) (* (sqrt 0.16666666666666666) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)))
73.0ms
(* (* 2.0 PI) u2)
1.0s
(* (sqrt 0.16666666666666666) (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5))

simplify1.4s

Counts
130 → 130
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02022066
15231904
220771656
done50001631

prune647.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes475.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01920
12618
22718
done2718

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.0s8000×body80valid
261.0ms8000×pre80true