Details

sample144.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	18	19
1	35	18
2	72	18
3	156	18
4	450	18
5	1407	18
done	5000	18

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (/ 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))

rewrite85.0ms

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`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

1.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
10.0ms	(pow (* -2.0 (log u1)) 0.5)
42.0ms	(* (* 2.0 PI) u2)
26.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

682.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
454.0ms	(pow (* -2.0 (log u1)) 0.5)
58.0ms	(* (* 2.0 PI) u2)
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.8s

Counts

104 → 104

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	197	1340
1	447	1286
2	1439	1166
done	5000	1147

prune547.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* 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)

rewrite69.0ms

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`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `sqr-pow`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `frac-2neg` `associate-l` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 89

Calls

4 calls:

1.0ms	(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
12.0ms	(pow (* -2.0 (log u1)) 0.5)
17.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
26.0ms	(* (* 2.0 PI) u2)

series2.1s

Counts

4 → 12

Calls

4 calls:

665.0ms	(fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5)
372.0ms	(pow (* -2.0 (log u1)) 0.5)
1.0s	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
43.0ms	(* (* 2.0 PI) u2)

simplify3.3s

Counts

101 → 101

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	189	1291
1	383	1246
2	1163	1146
3	4195	1127
done	5000	1126

prune653.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
106×	`times-frac`
102×	`sqrt-prod`
65×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqr-pow`
27×	`add-exp-log`
25×	`associate-r`
24×	`pow1` `swap-sqr`
23×	`associate-l`
20×	`unpow-prod-down`
16×	`unswap-sqr`
15×	`add-cbrt-cube`
10×	`associate-/l*`
8×	`sqrt-pow1` `pow1/2` `div-exp`
6×	`pow-prod-down` `prod-exp` `associate-/r*` `div-inv`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num` `*-commutative`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 214

Calls

4 calls:

10.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
9.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
17.0ms	(* (* 2.0 PI) u2)
46.0ms	(* (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))

series3.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.4s	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
73.0ms	(* (* 2.0 PI) u2)
1.2s	(* (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))

simplify1.5s

Counts

226 → 226

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	292	4574
1	491	3516
2	1654	3305
done	5000	3268

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* 1.0 (pow (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (/ 1 2))) (cos (* (* 2.0 PI) u2)) 0.5)
0.1b	(pow (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (/ 1 2))
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
19×	`times-frac`
17×	`pow-exp`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
15×	`prod-exp`
14×	`add-cbrt-cube`
13×	`pow-unpow`
12×	`unpow-prod-down`
10×	`pow1`
5×	`pow-to-exp` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`associate-r` `pow-prod-down` `div-inv`
2×	`cbrt-undiv`
1×	`pow-pow` `frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `fma-udef`

Counts

4 → 106

Calls

4 calls:

1.0ms	(fma (* 1.0 (pow (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (/ 1 2))) (cos (* (* 2.0 PI) u2)) 0.5)
36.0ms	(pow (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (/ 1 2))
37.0ms	(* (* 2.0 PI) u2)
29.0ms	(/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0))

series3.2s

Counts

4 → 12

Calls

4 calls:

715.0ms	(fma (* 1.0 (pow (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (/ 1 2))) (cos (* (* 2.0 PI) u2)) 0.5)
1.4s	(pow (/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0)) (/ 1 2))
55.0ms	(* (* 2.0 PI) u2)
1.1s	(/ (pow (* -2.0 (log u1)) (* 2 0.5)) (* 6.0 6.0))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	240	2216
1	558	1986
2	1552	1780
done	5000	1567

prune658.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes630.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	26
1	31	24
done	31	24

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
226.0ms	8000×	pre	80	true