Details

Time bar (total: 30.7s)

sample194.0ms

Algorithm
intervals
Results
43.0ms256×body80valid
8.0ms256×pre80true

simplify3.9s

Counts
1 → 1
Iterations
IterNodes
done5000
51408
4387
3148
272
135
018

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize55.0ms

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)
0.4b
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite152.0ms

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:
91.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
5.0ms
(pow (* -2.0 (log u1)) 0.5)
14.0ms
(* (* 2.0 PI) u2)
34.0ms
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts
4 → 12
Calls
4 calls:
641.0ms
(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
426.0ms
(pow (* -2.0 (log u1)) 0.5)
60.0ms
(* (* 2.0 PI) u2)
1.2s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.6s

Counts
108 → 108
Iterations
IterNodes
done5008
21853
1571
0214

prune787.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize36.0ms

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)
0.2b
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite102.0ms

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:
53.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
5.0ms
(pow (* -2.0 (log u1)) 0.5)
27.0ms
(* (* 2.0 PI) u2)
14.0ms
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series2.3s

Counts
4 → 12
Calls
4 calls:
692.0ms
(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
428.0ms
(pow (* -2.0 (log u1)) 0.5)
63.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify1.8s

Counts
105 → 105
Iterations
IterNodes
done5002
21650
1512
0206

prune721.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* PI u2) (* PI u2)) (* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.3333333333333333))
0.2b
(fma 0.16666666666666666 (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.5)
0.2b
(* (* PI u2) (* PI u2))
0.3b
(* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.3333333333333333)

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
346×add-exp-log
303×prod-exp
96×pow-exp
61×pow1
59×add-cbrt-cube
42×pow-to-exp
40×cbrt-unprod
30×pow-prod-down
9×add-sqr-sqrt
7×associate-*l*
6×*-un-lft-identity add-cube-cbrt
5×associate-*r*
4×expm1-log1p-u pow-sqr pow-prod-up log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus unswap-sqr sqr-pow
1×pow2 unpow-prod-down swap-sqr fma-udef
Counts
4 → 171
Calls
4 calls:
102.0ms
(* (* (* PI u2) (* PI u2)) (* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.3333333333333333))
0.0ms
(fma 0.16666666666666666 (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.5)
43.0ms
(* (* PI u2) (* PI u2))
39.0ms
(* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.3333333333333333)

series3.1s

Counts
4 → 12
Calls
4 calls:
456.0ms
(* (* (* PI u2) (* PI u2)) (* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.3333333333333333))
1.5s
(fma 0.16666666666666666 (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.5)
98.0ms
(* (* PI u2) (* PI u2))
1.1s
(* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.3333333333333333)

simplify2.2s

Counts
183 → 183
Iterations
IterNodes
done5005
21807
1500
0207

prune880.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b
(* (* 2.0 PI) u2)
0.3b
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
0.4b
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
76×add-exp-log
43×add-sqr-sqrt times-frac
34×prod-exp
32×*-un-lft-identity add-cube-cbrt
22×associate-*r* pow-exp
20×div-exp
16×add-cbrt-cube
14×sqr-pow
13×pow-unpow
12×pow1
11×pow-to-exp
9×unpow-prod-down
6×associate-*l* unswap-sqr
5×cbrt-unprod associate-/l*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×associate-/r* div-inv
2×cbrt-undiv pow-pow *-commutative
1×clear-num frac-2neg associate-*r/
Counts
4 → 152
Calls
4 calls:
12.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
27.0ms
(* (* 2.0 PI) u2)
14.0ms
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
35.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
434.0ms
(pow (* -2.0 (log u1)) (/ 0.5 2))
41.0ms
(* (* 2.0 PI) u2)
1.1s
(/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0)
974.0ms
(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (/ (pow (* -2.0 (log u1)) (/ 0.5 2)) 6.0))

simplify2.1s

Counts
164 → 164
Iterations
IterNodes
done5000
21997
1622
0246

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes782.0ms

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
done24
124
018

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.6s8000×body80valid
718.0ms8000×pre80true