Details

Time bar (total: 45.8s)

sample176.0ms

Algorithm
intervals
Results
49.0ms256×body80valid
8.0ms256×pre80true

simplify7.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
018628
135603
272603
3148603
4387603
51408603
done5000603

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×*-un-lft-identity add-cbrt-cube associate-*l* prod-exp add-cube-cbrt
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 sum-log fma-def flip3-+ associate-*l/ flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
73.0ms
(+ (* (* (/ 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)
26.0ms
(* (* 2.0 PI) u2)
26.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts
4 → 12
Calls
4 calls:
737.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
408.0ms
(pow (* -2.0 (log u1)) 0.5)
59.0ms
(* (* 2.0 PI) u2)
1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.9s

Counts
108 → 108
Iterations

Useful iterations: done (2.9s)

IterNodesCost
021449757
157147007
2185346196
done500845866

prune807.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×times-frac
12×pow1
11×add-cbrt-cube
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×expm1-log1p-u div-exp pow-prod-down pow-exp log1p-expm1-u
3×pow-unpow associate-/r* associate-*r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative clear-num sum-log fma-def frac-2neg flip3-+ associate-*l* *-commutative flip-+ div-inv
Counts
4 → 93
Calls
4 calls:
65.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
10.0ms
(pow (* -2.0 (log u1)) 0.5)
14.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
27.0ms
(* (* 2.0 PI) u2)

series2.2s

Counts
4 → 12
Calls
4 calls:
645.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
426.0ms
(pow (* -2.0 (log u1)) 0.5)
1.0s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
59.0ms
(* (* 2.0 PI) u2)

simplify2.6s

Counts
105 → 105
Iterations

Useful iterations: done (2.6s)

IterNodesCost
020650197
151047723
2159547458
done500047008

prune795.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))
0.9b
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-sqr-sqrt
14×*-un-lft-identity add-cbrt-cube associate-*l* prod-exp add-cube-cbrt
12×pow1
11×times-frac
8×associate-*r*
6×pow-exp
5×cbrt-unprod log1p-expm1-u
4×expm1-log1p-u div-exp pow-prod-down add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv expm1-log1p associate-*l/ div-inv expm1-udef
Counts
4 → 93
Calls
4 calls:
18.0ms
(pow (* -2.0 (log u1)) 0.5)
15.0ms
(* (* 2.0 PI) u2)
22.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0ms
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

series2.8s

Counts
4 → 12
Calls
4 calls:
421.0ms
(pow (* -2.0 (log u1)) 0.5)
76.0ms
(* (* 2.0 PI) u2)
1.1s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.2s
(expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

simplify4.7s

Counts
105 → 105
Iterations

Useful iterations: 3 (2.6s)

IterNodesCost
018544176
145542206
2133841580
3484041250
done500141250

prune843.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize147.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))
0.4b
(/ (fma (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* 0.5 (* 0.5 0.5))) (+ (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))))
0.6b
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
0.6b
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
622×add-exp-log
434×prod-exp
232×pow1
166×add-cbrt-cube
132×pow-prod-down
113×div-exp
112×cbrt-unprod
56×pow-exp
30×associate-*l/ associate-*r/
28×pow-to-exp
18×pow-sqr pow-prod-up
17×cbrt-undiv
12×add-sqr-sqrt *-un-lft-identity frac-add add-cube-cbrt
9×times-frac add-log-exp
8×associate-/r/
6×frac-times pow-plus flip3-- flip--
4×expm1-log1p-u log1p-expm1-u
3×associate-+r+ associate-/r* associate-/l*
2×pow2 sum-log flip3-+ swap-sqr associate-*r* associate-*l* *-commutative flip-+
1×+-commutative clear-num associate-+r- sub-neg fma-def frac-2neg diff-log prod-diff div-inv
Counts
4 → 286
Calls
4 calls:
285.0ms
(+ (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))
509.0ms
(/ (fma (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* 0.5 (* 0.5 0.5))) (+ (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))))
362.0ms
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
376.0ms
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

series4.9s

Counts
4 → 12
Calls
4 calls:
860.0ms
(+ (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)))
2.3s
(/ (fma (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* 0.5 (* 0.5 0.5))) (+ (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (- (* 0.5 0.5) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))))
1.1s
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
597.0ms
(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

simplify7.2s

Counts
298 → 298
Iterations

Useful iterations: done (7.0s)

IterNodesCost
0374268789
11102233842
24427213096
done5000213016

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes746.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
020788
126788
done26788

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s8000×body80valid
246.0ms8000×pre80true