Details

Time bar (total: 32.6s)

sample276.0ms

Algorithm
intervals
Results
68.0ms256×body80valid
14.0ms256×pre80true

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
63527
51264
4443
3158
271
136
018

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ 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))

rewrite57.0ms

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:
21.0ms
(+ 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)
22.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.4s

Counts
4 → 12
Calls
4 calls:
504.0ms
(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
824.0ms
(pow (* -2 (log u1)) 0.5)
43.0ms
(* PI u2)
1.1s
(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.8s

Counts
85 → 85
Iterations
IterNodes
34270
21098
1383
0164

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

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:
10.0ms
(pow (* -2 (log u1)) 0.5)
20.0ms
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
33.0ms
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
8.0ms
(* PI u2)

series2.6s

Counts
4 → 12
Calls
4 calls:
405.0ms
(pow (* -2 (log u1)) 0.5)
1.1s
(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
1.1s
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
25.0ms
(* PI u2)

simplify1.0s

Counts
102 → 102
Iterations
IterNodes
32473
2863
1314
0145

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (log u1) -2) 0.5)
0.3b
(* PI u2)
0.4b
(* (pow (* (log u1) -2) 0.5) 1/6)
1.0b
(exp (* (pow (* (log u1) -2) 0.5) 1/6))

rewrite48.0ms

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-*l*
7×prod-exp
6×associate-*r* 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×exp-prod exp-to-pow rem-exp-log
Counts
4 → 72
Calls
4 calls:
10.0ms
(pow (* (log u1) -2) 0.5)
6.0ms
(* PI u2)
12.0ms
(* (pow (* (log u1) -2) 0.5) 1/6)
19.0ms
(exp (* (pow (* (log u1) -2) 0.5) 1/6))

series2.6s

Counts
4 → 12
Calls
4 calls:
351.0ms
(pow (* (log u1) -2) 0.5)
23.0ms
(* PI u2)
1.1s
(* (pow (* (log u1) -2) 0.5) 1/6)
1.1s
(exp (* (pow (* (log u1) -2) 0.5) 1/6))

simplify3.1s

Counts
84 → 84
Iterations
IterNodes
45568
31807
2688
1276
0133

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite375.0ms

Algorithm
rewrite-expression-head
Rules
202×add-exp-log
166×prod-exp
46×add-cbrt-cube
43×pow1
29×cbrt-unprod
28×pow-exp
23×add-sqr-sqrt
17×*-un-lft-identity pow-prod-down add-cube-cbrt
14×pow-to-exp
12×times-frac
11×associate-*r*
7×associate-*l*
4×pow-sqr pow-prod-up insert-posit16 associate-/l* add-log-exp difference-of-squares unswap-sqr sqr-pow
3×associate-/r* *-commutative
2×unpow-prod-down pow-plus flip3-- associate-/r/ flip-- associate-/l/
1×pow2 cbrt-undiv clear-num frac-2neg div-sub swap-sqr div-exp div-inv
Counts
4 → 157
Calls
4 calls:
22.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
21.0ms
(* 1/6 (pow (* -2 (log u1)) 0.5))
45.0ms
(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
280.0ms
(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))

series3.5s

Counts
4 → 12
Calls
4 calls:
1.1s
(* 1/6 (pow (* -2 (log u1)) 0.5))
1.1s
(* 1/6 (pow (* -2 (log u1)) 0.5))
896.0ms
(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
430.0ms
(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))

simplify1.2s

Counts
169 → 169
Iterations
IterNodes
22566
1731
0275

prune3.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes415.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
225
125
018

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.1s8000×body80valid
418.0ms8000×pre80true