Details

Time bar (total: 12.2s)

sample330.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
5.0ms256×pre80true

simplify64.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03410
17110
215410
346910
4181210
5500110
done500110

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

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

rewrite110.0ms

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:
59.0ms
(+ (* (* (/ 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)
16.0ms
(* (* 2.0 PI) u2)
24.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts
4 → 12
Calls
4 calls:
459.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
257.0ms
(pow (* -2.0 (log u1)) 0.5)
38.0ms
(* (* 2.0 PI) u2)
690.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify60.0ms

Counts
99 → 99
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0507728
12155656
25001656
done5001656

prune324.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

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

rewrite81.0ms

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
6×add-log-exp
5×div-exp
4×pow-prod-down pow-exp cbrt-unprod
3×pow-unpow times-frac associate-*r* associate-/r*
2×cbrt-undiv pow-to-exp pow-pow
1×+-commutative unpow-prod-down frac-2neg flip3-+ associate-*l* clear-num sum-log *-commutative flip-+ div-inv associate-/l* sqr-pow
Counts
4 → 70
Calls
4 calls:
38.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms
(pow (* -2.0 (log u1)) 0.5)
20.0ms
(* (* 2.0 PI) u2)
14.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
458.0ms
(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
255.0ms
(pow (* -2.0 (log u1)) 0.5)
38.0ms
(* (* 2.0 PI) u2)
679.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify53.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0456597
12028527
25001525
done5001525

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite772.0ms

Algorithm
rewrite-expression-head
Rules
342×add-exp-log
213×prod-exp
96×add-cbrt-cube
81×div-exp
50×cbrt-unprod
43×pow1
32×pow-exp
21×cbrt-undiv
18×times-frac
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-prod-down
16×pow-to-exp
9×associate-/r*
6×associate-/l*
5×associate-*l/
4×pow-sqr pow-prod-up add-log-exp difference-of-squares
3×frac-2neg clear-num div-inv
2×flip3-- pow-plus associate-/r/ flip-- associate-/l/
1×pow2 frac-times div-sub associate-*r/ swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 178
Calls
4 calls:
14.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
14.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
502.0ms
(/ (- (* (* (/ (* 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))
231.0ms
(* (* (/ (* 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))))

series2.6s

Counts
4 → 12
Calls
4 calls:
696.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
674.0ms
(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
752.0ms
(/ (- (* (* (/ (* 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))
450.0ms
(* (* (/ (* 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))))

simplify110.0ms

Counts
190 → 190
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08973821
141392864
250022794
done50022794

prune491.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* u2 PI)
0.2b
(* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))))
0.3b
(/ (- 0.25 (* 0.05555555555555555 (* (pow (cos (* 2.0 (* u2 PI))) 2) (log (/ 1 u1))))) (- (* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI))))) 0.5))
0.3b
(* 0.05555555555555555 (* (pow (cos (* 2.0 (* u2 PI))) 2) (log (/ 1 u1))))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
147×add-exp-log
132×prod-exp
60×pow-exp
52×distribute-rgt-in log-prod distribute-lft-in
46×add-sqr-sqrt
45×times-frac
44×add-cube-cbrt *-un-lft-identity
30×pow-to-exp
18×add-cbrt-cube
10×pow1
9×associate-*l*
7×cbrt-unprod
5×associate-*r* div-inv
4×add-log-exp
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×flip3-- associate-/r/ distribute-rgt-neg-out flip-- associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp log-rec clear-num unswap-sqr
Counts
4 → 171
Calls
4 calls:
7.0ms
(* u2 PI)
105.0ms
(* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))))
143.0ms
(/ (- 0.25 (* 0.05555555555555555 (* (pow (cos (* 2.0 (* u2 PI))) 2) (log (/ 1 u1))))) (- (* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI))))) 0.5))
75.0ms
(* 0.05555555555555555 (* (pow (cos (* 2.0 (* u2 PI))) 2) (log (/ 1 u1))))

series1.7s

Counts
4 → 12
Calls
4 calls:
20.0ms
(* u2 PI)
607.0ms
(* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))))
930.0ms
(/ (- 0.25 (* 0.05555555555555555 (* (pow (cos (* 2.0 (* u2 PI))) 2) (log (/ 1 u1))))) (- (* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI))))) 0.5))
105.0ms
(* 0.05555555555555555 (* (pow (cos (* 2.0 (* u2 PI))) 2) (log (/ 1 u1))))

simplify112.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
010823373
137593147
250013109
done50013109

prune572.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes322.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410
done2410

end0.0ms

sample953.0ms

Algorithm
intervals
Results
632.0ms8000×body80valid
116.0ms8000×pre80true