Details

sample264.0ms

Algorithm

intervals

Results

127.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (268.0ms)

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))

rewrite100.0ms

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:

0.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
7.0ms	(pow (* -2.0 (log u1)) 0.5)
29.0ms	(* (* 2.0 PI) u2)
60.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.5s

Counts

4 → 12

Calls

4 calls:

742.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
456.0ms	(pow (* -2.0 (log u1)) 0.5)
75.0ms	(* (* 2.0 PI) u2)
1.3s	(* (/ 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

prune553.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 120

Calls

4 calls:

7.0ms	(pow (* -2.0 (log u1)) 0.5)
89.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
33.0ms	(* (* 2.0 PI) u2)
55.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.8s

Counts

4 → 12

Calls

4 calls:

428.0ms	(pow (* -2.0 (log u1)) 0.5)
1.2s	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
50.0ms	(* (* 2.0 PI) u2)
1.1s	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify2.3s

Counts

132 → 132

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	208	1857
1	450	1623
2	1428	1494
done	5001	1485

prune868.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
0.1b	(* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))
0.2b	(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (- 0.16666666666666666 (* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))))
0.3b	(* (pow u2 2) (pow PI 2))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
58×	`prod-exp`
44×	`pow-exp`
33×	`add-sqr-sqrt`
26×	`pow-to-exp`
18×	`unswap-sqr`
16×	`unpow-prod-down` `associate-l`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-cbrt-cube` `sqr-pow`
12×	`associate-r`
10×	`unpow2`
7×	`pow1`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `*-commutative`
2×	`sub-neg` `pow-pow` `associate-*r/`
1×	`flip3--` `flip--`

Counts

4 → 152

Calls

4 calls:

10.0ms	(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
45.0ms	(* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))
64.0ms	(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (- 0.16666666666666666 (* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))))
46.0ms	(* (pow u2 2) (pow PI 2))

series2.9s

Counts

4 → 12

Calls

4 calls:

1.4s	(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
88.0ms	(* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))
1.3s	(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (- 0.16666666666666666 (* 0.3333333333333333 (* (pow u2 2) (pow PI 2)))))
59.0ms	(* (pow u2 2) (pow PI 2))

simplify1.9s

Counts

164 → 164

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	275	2982
1	636	2753
2	1925	2422
done	5000	2384

prune623.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
0.6b	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
24×	`prod-exp`
23×	`add-cbrt-cube`
19×	`sqrt-prod`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`associate-l`
15×	`times-frac`
14×	`pow1`
9×	`cbrt-unprod`
6×	`div-exp` `pow-exp` `associate-/r*`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-unpow`
2×	`pow-pow` `sqrt-div` `associate-l/` `-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

15.0ms	(pow (* -2.0 (log u1)) 0.5)
24.0ms	(* (* 2.0 PI) u2)
62.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
44.0ms	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

series3.1s

Counts

4 → 12

Calls

4 calls:

411.0ms	(pow (* -2.0 (log u1)) 0.5)
74.0ms	(* (* 2.0 PI) u2)
1.3s	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
1.3s	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

simplify1.6s

Counts

122 → 122

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	229	1900
1	516	1728
2	1768	1579
done	5000	1570

prune712.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes390.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	24
1	24	24
done	24	24

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
316.0ms	8000×	pre	80	true