Details

Time bar (total: 26.5s)

sample195.0ms

Algorithm
intervals
Results
53.0ms256×body80valid
9.0ms256×pre80true

simplify1.7s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize116.0ms

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))

rewrite165.0ms

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×div-exp pow-prod-down unswap-sqr sqr-pow
3×pow-to-exp pow-unpow
2×unpow-prod-down pow-pow *-commutative
1×cbrt-undiv +-commutative flip3-+ associate-*l/ sum-log flip-+ div-inv
Counts
4 → 87
Calls
4 calls:
71.0ms
(+ (* (* (/ 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)
34.0ms
(* (* 2.0 PI) u2)
48.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts
4 → 12
Calls
4 calls:
617.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
422.0ms
(pow (* -2.0 (log u1)) 0.5)
56.0ms
(* (* 2.0 PI) u2)
1.2s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.1s

Counts
99 → 99

prune568.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (* 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 add-cube-cbrt *-un-lft-identity
15×times-frac
12×pow1
11×add-cbrt-cube
6×add-log-exp
5×unpow-prod-down prod-exp associate-/l* sqr-pow
4×div-exp pow-prod-down pow-exp
3×pow-unpow associate-*r* associate-/r* cbrt-unprod
2×pow-to-exp pow-pow
1×cbrt-undiv +-commutative frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv
Counts
4 → 84
Calls
4 calls:
61.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
8.0ms
(pow (* -2.0 (log u1)) 0.5)
17.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
33.0ms
(* (* 2.0 PI) u2)

series2.2s

Counts
4 → 12
Calls
4 calls:
668.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
358.0ms
(pow (* -2.0 (log u1)) 0.5)
1.2s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
52.0ms
(* (* 2.0 PI) u2)

simplify893.0ms

Counts
96 → 96

prune535.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b
(/ 6.0 (pow (* -2.0 (log u1)) (/ 0.5 2)))
0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ 6.0 (pow (* -2.0 (log u1)) (/ 0.5 2))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
209×times-frac
96×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
76×add-exp-log
43×unpow-prod-down sqr-pow
40×div-exp
24×associate-/r*
22×pow-exp
16×add-cbrt-cube
14×prod-exp
13×pow-unpow
12×pow1
11×pow-to-exp
9×div-inv
8×associate-/l*
4×cbrt-undiv pow-prod-down add-log-exp
3×associate-*r* cbrt-unprod
2×pow-pow frac-2neg clear-num
1×associate-*l* associate-/r/ *-commutative
Counts
4 → 235
Calls
4 calls:
10.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
14.0ms
(/ 6.0 (pow (* -2.0 (log u1)) (/ 0.5 2)))
24.0ms
(* (* 2.0 PI) u2)
35.0ms
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ 6.0 (pow (* -2.0 (log u1)) (/ 0.5 2))))

series2.8s

Counts
4 → 12
Calls
4 calls:
373.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
1.2s
(/ 6.0 (pow (* -2.0 (log u1)) (/ 0.5 2)))
69.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ 6.0 (pow (* -2.0 (log u1)) (/ 0.5 2))))

simplify2.3s

Counts
247 → 247

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 2.0 PI) u2)
0.3b
(/ (+ (pow (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 3) (pow 0.5 3)) (+ (* 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))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))))
0.5b
(* (* (* 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))))
0.7b
(pow (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 3)

rewrite920.0ms

Algorithm
rewrite-expression-head
Rules
341×add-exp-log
232×prod-exp
129×pow1
101×add-cbrt-cube
72×pow-prod-down
64×cbrt-unprod
61×div-exp
37×pow-exp
24×*-un-lft-identity
22×associate-*r/
16×add-sqr-sqrt pow-to-exp add-cube-cbrt associate-*l/
15×times-frac
10×cbrt-undiv
9×pow-sqr pow-prod-up
8×associate-/r/
6×frac-add
5×associate-/l*
4×associate-*r* sum-cubes distribute-lft-out add-log-exp rem-cube-cbrt
3×frac-times pow-unpow flip3-- pow-pow pow-plus associate-/r* flip--
2×flip3-+ associate-*l* *-commutative flip-+ associate-/l/
1×cube-div pow2 cube-mult unpow-prod-down frac-2neg unpow3 cube-prod swap-sqr clear-num div-inv sqr-pow
Counts
4 → 204
Calls
4 calls:
18.0ms
(* (* 2.0 PI) u2)
340.0ms
(/ (+ (pow (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 3) (pow 0.5 3)) (+ (* 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))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))))
438.0ms
(* (* (* 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))))
92.0ms
(pow (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 3)

series3.4s

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (* 2.0 PI) u2)
2.0s
(/ (+ (pow (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 3) (pow 0.5 3)) (+ (* 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))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))))
710.0ms
(* (* (* 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))))
639.0ms
(pow (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 3)

simplify761.0ms

Counts
216 → 216

prune985.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes557.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify928.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.4s8000×body80valid
224.0ms8000×pre80true