Details

Time bar (total: 37.5s)

sample176.0ms

Algorithm
intervals
Results
83.0ms256×body80valid
11.0ms256×pre80true

simplify4.0s

Counts
1 → 1
Iterations
IterNodes
done5000
51530
4489
3158
271
136
018

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.1b
(pow (* -2 (log u1)) 0.5)
0.3b
(* PI u2)
0.4b
(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
14×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube associate-*r*
7×prod-exp
6×associate-*l* add-log-exp
4×pow-exp insert-posit16
3×pow-unpow unswap-sqr sqr-pow
2×pow-to-exp unpow-prod-down pow-pow pow-prod-down *-commutative cbrt-unprod
1×+-commutative sum-log flip3-+ flip-+
Counts
4 → 73
Calls
4 calls:
14.0ms
(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
5.0ms
(pow (* -2 (log u1)) 0.5)
6.0ms
(* PI u2)
13.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))

series1.9s

Counts
4 → 12
Calls
4 calls:
482.0ms
(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
383.0ms
(pow (* -2 (log u1)) 0.5)
23.0ms
(* PI u2)
1.0s
(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify3.5s

Counts
85 → 85
Iterations
IterNodes
done5000
34829
21216
1425
0164

prune457.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2 (log u1)) 0.5)
0.2b
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.3b
(* PI u2)
0.3b
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
20×add-sqr-sqrt
17×prod-exp
15×associate-*l*
13×add-cbrt-cube
12×*-un-lft-identity add-cube-cbrt
11×pow1
9×associate-*r*
8×sqrt-prod
6×pow-exp
5×cbrt-unprod unswap-sqr
4×insert-posit16 add-log-exp sqr-pow
3×pow-to-exp pow-unpow pow-prod-down *-commutative
2×unpow-prod-down pow-pow
Counts
4 → 90
Calls
4 calls:
6.0ms
(pow (* -2 (log u1)) 0.5)
34.0ms
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
6.0ms
(* PI u2)
14.0ms
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.5s

Counts
4 → 12
Calls
4 calls:
379.0ms
(pow (* -2 (log u1)) 0.5)
1.1s
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
32.0ms
(* PI u2)
988.0ms
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify2.5s

Counts
102 → 102
Iterations
IterNodes
done5000
33262
2978
1352
0145

prune721.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) 0.5)
0.1b
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)
0.3b
(* PI u2)
0.4b
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
64×prod-exp
48×pow-exp
21×pow-to-exp
11×add-cbrt-cube
10×add-sqr-sqrt
8×*-un-lft-identity associate-*r* add-cube-cbrt
7×pow1
6×add-log-exp
4×associate-*l* cbrt-unprod insert-posit16
3×pow-unpow
2×unpow-prod-down pow-pow pow-prod-down *-commutative sqr-pow
1×+-commutative sum-log flip3-+ flip-+ unswap-sqr
Counts
4 → 98
Calls
4 calls:
105.0ms
(+ (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) 0.5)
25.0ms
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)
11.0ms
(* PI u2)
136.0ms
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))

series2.7s

Counts
4 → 12
Calls
4 calls:
483.0ms
(+ (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) 0.5)
1.7s
(pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)
40.0ms
(* PI u2)
457.0ms
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))

simplify3.8s

Counts
110 → 110
Iterations
IterNodes
done5002
21693
1588
0219

prune666.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))
0.4b
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))
0.4b
(/ (- (* (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))) (* 0.5 0.5)) (- (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) 0.5))
0.5b
(* (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
3433×prod-exp
3384×add-exp-log
1664×pow-exp
728×pow-to-exp
52×add-cbrt-cube
33×cbrt-unprod
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
11×pow1 associate-*r*
4×insert-posit16 associate-/l* add-log-exp difference-of-squares
3×associate-/r* associate-*l* *-commutative
2×unpow-prod-down flip3-- associate-/r/ flip-- sqr-pow associate-/l/
1×pow2 cbrt-undiv clear-num frac-2neg pow-plus div-sub swap-sqr div-exp pow-prod-down pow-sqr pow-prod-up div-inv
Counts
4 → 770
Calls
4 calls:
115.0ms
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))
122.0ms
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))
883.0ms
(/ (- (* (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))) (* 0.5 0.5)) (- (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) 0.5))
412.0ms
(* (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)))

series2.3s

Counts
4 → 12
Calls
4 calls:
480.0ms
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))
478.0ms
(* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))
829.0ms
(/ (- (* (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5))) (* 0.5 0.5)) (- (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) 0.5))
535.0ms
(* (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)) (* (* 1/6 (cos (* 2 (* PI u2)))) (pow (* (pow (+ 0 (log u1)) 1.0) (pow -2 1.0)) 0.5)))

simplify4.1s

Counts
782 → 782
Iterations
IterNodes
done5000
23540
11257
0439

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes435.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done25
125
018

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.2s8000×body80valid
432.0ms8000×pre80true